Brother left a nursing facility without being discharged. He has a lot of things going on w/ illnesses & can't take care of himself. Advice?

Does your Mom want to care for him? If not, call APS and ask that they do an evaluation. Mom needs to tell the Caseworker that she cannot care for her son nor can she support him.

Yes if he is competent he can leave against Against Medical Advice. But, if he was determined 24/7 care, its considered "unsafe" to allow him to leave. He would need to prove he had 24/7 care at home. Going to a 92 yr old woman's home is not safe.

Was the NH he was in, suck?

Unless your brother has a diagnosis of cognitive incapacity he can discharge himself at any time and if you're not his PoA or guardian you don't have any power in this situation except to call Adult Protective Services for both of them. If you are DPoA for your mother you have authority to act on her behalf.