Can you claim your 91 year old mother who lives with you and you care for and she gets social security?

Probably. She has to meet all the criteria. She is not required to live with you.

Here is a checklist for determining whether a relative qualifies.

• Do they live with you? Your relative must live at your residence all year or be on the list of “relatives who do not live with you” in Publication 501. About 30 types of relatives are on this list.
• Do they make less than $4,300 in 2020 or 2021? Your relative cannot have a gross income of more than $4,300 in 2020 or 2021 and be claimed by you as a dependent.
• Do you financially support them? You must provide more than half of your relative’s total support each year.
• Are you the only person claiming them? This means you can’t claim the same person twice, once as a qualifying relative and again as a qualifying child. It also means you can’t claim a relative—say a cousin—if someone else, such as his parents, also claims him.