My mother lives on her own. She earns about $3,000 a year from Social Security and my husband and I pay her rent and help buy groceries. Can we claim her as a dependent?

Possibly. If her gross income is less than $4,050 and you pay more than half of her support, then you may be able to claim her as a dependent. She does not need to live with you. (26 CFR § 1.36B-1(f); 26 CFR § 1.152-1; CBPP, Health Care Assister's Guide to Tax Rules, updated Feb. 2016).