Can be sued if on ssi in Alabama for breaking a lease

Please explain.

Yes, I believe people can be sued in Alabama, as they can be sued anywhere else. And the fact that you are on SSI doesn't make you immune from suit.

If your sole source of income is SSI, the plaintiff, if they obtain a judgment against you, probably wouldn't be able to collect, but that is another issue.

If you are thinking that being on SSI makes you immune from a law suit, you are thinking incorrectly. However it does make it harder to collect on the suit.