Yes, I actually remember more problems from the people who were in jails and somehow they got out when SHTF, then from the people who had mental problems.

Sometimes people from jail were recruited in different fractions and promised freedom later if they obey. Mostly they were very bad folks, and become even worse.
Sometimes some groups look for the meanest from them to recruit them.

Again, depends from the scenario and maybe region too, but those folks definitely gonna be problem.