My unemployed sister and her 4 year old lived with me for the year. Can I claim them both?

Maybe----but we need to know if your sister had any income----including unemployment benefits.    If your sister had more than $5050 of any income except for Social Security, you cannot claim her as a dependent.   Tell us more.

if as you posted the sister had no income and you provided more than half of her support you can claim her and the child as dependents.