It really depends on the mental illness. Most mentally ill people could do something, most of the time. What exactly they could do would depend on the particular illness. Many are not currently hireable because even one episode a week is enough to get them fired. Some are not currently hirable because they have been out of the workforce for so long, that they have lost a bunch of habits. I think that could be remedied.
But, as I said, if they are really incapable of any possible employment, then they should get treatment and supportive housing.
But, as I said, if they are really incapable of any possible employment, then they should get treatment and supportive housing.