Leaving is their own choise, government can't force them to be in.
But what the government can do is put the most amount of people inside shelters, with more shelters provided for everyone, it would be better than the current system, even if some give up and leave, most would stay. And making it feel like job center is a good thing, not a bad one. the porpuse of shelters should be a temporary place for people to stay, and find a better work later, not a place for someone to live forever. The current system helps people live inside the shelter, but leaving and finding a better job is extremelly difficult, because without some cash, surviving outside the shelter is difficult. The current system keeps people stuck in shelters forever, which is bad both economically, and also to the homeless people who will never have the chance for anything else in their lives
. Mandatory work can also serve as job training.