A mentally ill person, being unable to think clearly, may imagine that society has abandoned him and treated him like trash, when objectively nothing of the sort has happened.

One example that comes to mind:

One time I allowed a homeless person to use my home while I was gone for several days (this was not a random person, but someone I had become familiar with over the course of a few months as we both attended recovery meetings.)

When I returned, rather than thanking me, that person questioned me about things in my place that they felt were wrong and pointed to a lifestyle they disapproved of.

Needless to say, I showed them the door and said good luck.

It was not my job or responsibility to help this person get back on their feet. I had gone above and beyond already.

At some point, the mentally ill person, despite being mentally ill, must still bear some of the responsibililty themself and learn to use some social manners. Otherwise, they themselves will also "get what they deserve" (they will be abandoned by someone who initially wanted to help them).

(The above is just one example and not intended to be a one-size-fits-all scenario).

Until my later twenties didn't grock that burning bridges behind me was a bad idea.

There have been a few bridges that needed to be burnt and I am glad I did it. But, that is just me.

I guess my next question is this: What about someone who cannot 'bear some responsibility' for themselves? Should they be left out in the cold to die? Is dealing with a mind that cannot operate in our society grounds for complete dismissal from society? I find that disturbing.

If it had been, I probably would have tried to help them find shelter. Also I knew that they at least knew where to find other people who might be willing to help them, since they were attending meetings.

However, you have a point. No matter how mentally ill, as long as they are not a threat to others a person should at least be provided with a minimum amount of bare necessities by society if it (society) wants to be considered something more than a loose pack of wild animals - it's not like we couldn't afford it if we didn't spend so much unnecessarily on the military.