There has been no comment from CBS, series producer Warner Bros. Television or Sheen whether the 45-year-old actor will be back to film the remaining eight episodes.
The Monday night show's finished episodes will air Feb. 7 and Feb. 14. To cover after that, CBS has ordered two extra episodes of "Rules of Engagement" and may increase its order for another sitcom as well as rely on "Two and Half Men" repeats.
No other comedy has the drawing power of "Men," which even in reruns averages bigger audiences (10.6 million, according to the Nielsen Co.) than first-run episodes of other network comedies, except for ABC's "Modern Family" (14.6 million).
Original episodes of "Two and a Half Men" top 15 million viewers and the show has increased its audience by 2 percent over last season, according to Nielsen. Sheen signed a new two-year contract at the end of last season that makes him one of the highest-paid actors on prime-time TV.
But he has been living on the edge, with a wild night in October that left a New York hotel room in shambles and sent him to a hospital, and a guilty plea last summer to assaulting his wife in Aspen, Colorado.
Sheen filled gossip pages again in January by spending a weekend partying hard in Las Vegas.
"I'm checking TMZ, as I do every day, to know if I have to go to work at all," his co-star, Jon Cryer, quipped on TBS' "Conan" last week.
At risk are both Sheen health and the wealth he generates for himself, CBS and Warner. CBS' advertising revenue for "Two and a Half Men" exceeds the $4 million licensing fee the network pays the studio for each episode.
According to the latest data from analysts at Kantar Media, "Men" brought in $161.6 million in ad revenue in 2009 and $113.8 million in revenue for the first nine months of 2010.
But given the hefty licensing fee CBS pays for the show, and the fact that CBS is the most watched network with a number of hit shows, its fate is not linked to a single program such as "Men." The sitcom also serves as anchor for the network's Monday comedy lineup.
For Warner, the sitcom is a true windfall: It's the studio's most successful show in syndication because it was also sold to the FX cable channel, said syndication expert Bill Carroll of Katz Media.
Based on a combination of the FX deal and syndication agreements, the sitcom's value to Warner could reach $600 million over the next several years, Carroll estimated. The current syndication contracts run thorough 2014 and deals are in place that will keep the show on in major markets through 2021.
With more than 150 episodes completed, "in terms of the durability of the show, it's probably in reasonably good shape" even if production ends now, Carroll said.
In Hollywood, however, where more is more, there's scant reason to think CBS and Warner would want to stop wringing laughs and cash out of "Two and a Half Men."
Both are careful in addressing the issue. After an initial joint statement with CBS in which the companies and series executive producer Chuck Lorre expressed concern for Sheen and supported his decision to seek treatment, Warner declined comment.
CBS issued a statement Monday when asked about the financial impact of Sheen's crisis, saying, "Any immediate programming or financial implications pale in comparison to his long term health, safety and well being."
Looking ahead, the network said, any ratings declines will be "more than offset" by reduced programming costs for the season. The shutdown's financial impact is "not material" to the network, CBS said.
"Two and a Half Men," which debuted in 2003, stars Sheen as womanizing bachelor Charlie Harper, who lives with his neurotic brother, the divorced Alan (Cryer) and Alan's son, Jake (Angus T. Jones).
Warner and CBS would not address whether they would try to keep the show going if Sheen didn't return. But there is historical precedent for trying - and even succeeding.
"Cheers" star Shelley Long exited in 1987 after five years; the comedy went out in 1993 as a hit. At NBC, "The Office" is preparing for life next season without Steve Carell.
"Recasting principals in a show can help, actually, taking a show that's getting a little tired around the edges and renewing it," said Tim Brooks, a former network executive and co-author of "The Complete Directory to Prime Time Network and Cable TV Shows."
If Sheen leaves CBS and "Two and a Half Men," said Brooks, "it's almost a certainty they'd give it a try" without him.