This seems like a good idea to me. It saves the state money, reduces the many problems due to homeless alcoholics, and it lets those are beyond hope live out their last few years with as little suffering as possible given their situations.
My only reservation is that if they became a lot more common, then some people might make less of an effort to recover, and some people who might have recovered after their sixth failed attempt to stop drinking might not succeed in quitting. That seems like a worthwhile risk though given the huge benefits, and perhaps there would be ways to decrease that risk.
"Wet houses"-- subsidized housing for alcoholics (they need to get most of their own money for alcohol, but their other expenses are covered) might actually be a good idea. It's cheaper than trying to get them to stop drinking, arguably kinder than trying to get people to take on a very hard task that they aren't interested in, and leads to less collateral damage than having alcoholics couch-surfing or living on the street.
Utilitarians, what do you think?