Absolutely. As long as you qualify for each of them individually. Three states currently will offset your unemployment benefits by your Social Security (not the other way around) and they are...
I believe this answer is slightly incorrect -- "Yes, you can. Under "Non monetary Issues" > "Disqualifications" item (f) on page 5 of the Related Link below, Social Security benefits are excluded...
Yes. If you qualify for unemployment benefits in your state, you can also collect Social Security benefits as they are 2 separate and distinct programs that do not interfere with each other.