It has been known for some time that after the highly publicized, insane media frenzy that was Charlie Sheen 1) Going bat-shit insane and 2) Getting very aggressively fired from his starring role on the #1 comedy show in America (I know, sad) Two and a Half Men, the character he played would be written off the program.

Do'h Indeed.
Being the cash cow that it is, CBS is not content with just canceling the program after its biggest star has left, but is rather going to make bank since the entire ordeal has become a massive interest to the average American television consumer. The return to air will be massively hyped and will most likely do huge ratings numbers, mostly for the curiosity factor of seeing how Sheen will be written off the show, and how newcomer Ashton Kutcher will be written in to replace him. Subsequent episodes will fair moderately, as people become accostomed and still curious as to how the show will function with this new dynamic. Then, it will probably fall below Sheen levels, go on for two more years (at most) and final leave our airwaves, just in time for the "half-man" of the title to be, well, about 1 and a half men all by himself.

His name is Angus T. Jones. How can he NOT be fat?
But this is me getting ahead of myself. What I am interested in is how Sheen's character will be written off the show. If we compare the situation to the recent high-profile show departure of Steve Carell and The Office, we will see why the Two and a Half Men-situation is really quite interesting, and leaves Chuck Lorre and the writers of Two and a Half Men the opportunity to do something truly remarkable...
But they probably won't.

Disappointed Sea Otter is preemptively disappointed
Granted, reports have surfaced revealing the show's producers have been planning on running a scenario where Charlie's character dies, throwing around several possible deaths including the tried-but-true "car goes off a cliff" scenario. I must say, that this is a terrific surprise, and raises my interest slightly in watching this crappy show just to see how this is handled.

I am assuming this is what leads to the crash...
While this is a cool way to write the character off, the unique circumstances of Sheen's departure (the public firing, the post-firing media frenzy around Sheen including but not limited to his failed concert tour, blog, Twitter, intern...) really allow the writers to do something even more spectacular than just killing the character off. Let's look at why by comparing it to the departure of Steve Carrell from The Office, another highly publicized and popular writing off of a major character, though following a more traditional (yet acceptable) route.
Steve Carell deciding to leave The Office was sort of a no-brainer. His film career is taking off with several supporting and starring roles that have made him one of the biggest faces in comedic film today. So Carell left the show that made him a household name under amicable circumstances, and with plenty of time for the show's writers to craft an entire season arc around his departure, filled with guest spots and mystery replacements. All of this added up to a highly rated final episode for Michael Scott, the door open for a return (both in reality and within the show's fiction), and a well-received, satisfying write-off to a truly remarkable television character.

Steve Carell, off to shoot Evan Almighty 2: Ready For Gomorrah?
So what makes Sheen's departure different from Carell's, and how do those differences relate to their respective characters' being written off their shows? Since Steve Carell left on a good note, with hardly anyone really having a right to be angry, his character was given a glorious sendoff, with story options that allow for the character's return to Scranton. Michael Scott is simply moving to Colorado. It seems far too easy for his character to be brought back in some capacity that it will not be done (probably as soon as next season). This also plays into the fact that the show has recently built up a sizable supporting cast, and used guest stars like Will Ferrell, James Spader, Jim Carrey, Ray Ramono, and a bunch of others I really don't feel the need to mention, to help the transition of the show into the post-Steve Carell Era. All in all, the transition to this new phase was relatively smooth and precise, showing care for both the character and the actor playing him all along the way.

On the other, much more emotionally scarred side of the coin is...
Charlie Sheen. The public firing and necessary replacement of Sheen's character is one thing. But it is the fact that he is a character so integral to the (I can't believe I'm using this word for Two and a Half Men) plot, his character's absence cannot just be ignored or even replaced with another actor (both common television tropes for disappearing characters). I mean, Chuck Lorre kind of screwed himself there. Sheen's character is named 'Charlie' for Christ's sake. The 'character' Charlie Harper is basically the real Charlie Sheen, a hedonistic, alcoholic womanizer.


Drugs?.....
Excuse me..?
Are you in here for drugs....
Why are you here?
Drugs
Cool
So both ignoring and replacing were never an option. Also, since he was fired, there is no way for the character to reappear (played by Sheen, at least) to film any sort of departure like Carell on The Office. Once again, this places Lorre and those behind the show at a disadvantage with their options for having the character disappear. Whatever happens, due to Sheen's inability to be used in his own character's departure, whatever the writers come up with will have a lot of exposition. Think of it like this: if they go with the Charlie died route, they have to explain all this in dialogue because they can't show it. There will be a lot of phone calls with Alan going "Charlie did WHAT?!"
This is a major problem. One of the biggest rules in comedic writing and improv is "Show me, don't tell me." Too much exposition is a sure-fire way to bog down a script and completely lose the audience. If you MUST explain things, do show in a clever way with sharp, witty writing. Oh wait, this is Two and a Half Men. Yeah, you guys are in trouble. Allow me to put on my writing hat and help:

Writing Hat
HOW I WOULD WRITE OFF CHARLIE SHEEN'S CHARACTER:
Because lots of exposition is a necessary evil at this point (reasons above), I would embrace this, and go for an all out expositive mind-f&#k, ala Inception and Fight Club. Charlie Harper, or "Uncle Charlie" to Jake Harper (Angus T. Jones), is and always has been a figment of Alan Harper's (Jon Cryer) imagination, another identity he would slip into to combat his increasingly empty and pathetic life. The conceit of the show has always been very simple: Charlie is a womanizing playboy and Alan is his opposite and foil, an uptight, whipped, and cowardly man. The entire 177 episode run (JESUS!!) is based entirely around this fact. These two are polar opposites, forced to live together due to Alan's wife leaving him at the beginning of the series. And the kid is there to be the swing-weight between the two leads, giving stakes to their conflicts. Oh, and also to make fart jokes, I guess.

Not a far cry from Mr. Sheen
Think of how brilliant a move this would be. First, it makes total sense within the framework of the show (with some obvious contradictions, but it is a stupid sitcom, so no one would really care about 'canon'). Both Alan and Charlie as characters are entirely one-dimensional. The grief and stress from the divorce that begins the series leads Alan's character to create the womanizing Charlie. Or, the creation of the 'Charlie' persona of Alan is what caused the divorce in the first place. Either way is fine. Any incoherences in the plot (i.e. almost every character's acknowledgement of both Alan and Charlie as separate people) can be explained away in that the show is viewed through the mind of Alan, so all those occurrences were due to an untrustworthy narrator.

Tell me this man is not deranged?
This also leads to so many ways the show can comment upon the public media blitz surrounding the show and Charlie Sheen. The can make comments (through characters within the show) about how "Charlie never existed," or "You don't need Charlie," or "Charlie was bad for you and for all of us." Turn Charlie into the enemy, just as he already is in this real life scenario! While killing the character off in a car crash will lead to him eventually being forgotten, this scenario allows Charlie to continue as a presence on the show, in a sense. Of course, he will never appear in the flesh, but he can be referenced while Alan is 'rehabilitated' after having come to terms with this horrible truth. Hell, that new character Ashton Kutcher is playing can be his crazy live-in doctor/friend who is trying to make him better. The scenarios write themselves, as Ashton's character goes through various wacky schemes to keep Alan sane and a functioning member of society.

Why is this guy always taking pictures? Is he Peter Parker?
One final, massive advantage to all of this would be an increased interest in past episodes and reruns, currently killing in syndication all over the place. Just as everyone has to watch Fight Club twice to truly appreciate and understand everything, watching old episodes of Two and a Half Men would be an epic experience. Trying to explain away and contemplate how Alan is acting as both Alan and Charlie would be hysterical and add an entire new and deep dimension to an otherwise flat and tedious show.
You know what. That's what I'm going to do regardless of how the character is disposed of. And I ask all of you to do the same. If you ever find yourself watching an episode of Two and a Half Men, please, watch with the idea in the back of your head that Charlie is simply a Durden-esque persona of Alan Harper. This may be the only way I will ever enjoy Charlie Sheen again. EVER.