The best solution is to take care of them in one way or another. You can't "put" them in institutions because they don't pose a danger to themselves or to others. You could offer them some arrangement, though.

If they're mentally ill, can they really choose by themselves? There's not much point in making offers to someone who can't distinguish or understand their options. People with limited ability to make decisions or take care of themselves shouldn't be out on the streets.

Now, you can either give them a home and a caretaker individually (let's say, each of them gets a full-time social worker), or put all of them in the same place where they're taken care of as a group (aka an institution).