I take care of my mother who has had a stroke. She gets a retirement of $18,000 a year and SSI of$ 5,650 a year which totals out at $23,650 does she need to file taxes?

If the Social Security and SSI is her ONLY source of income, then, no, she has NO FEDERAL filing requirement.

The same probably applies for the state, but I am not sure since you failed to identify the state.