Unemployment rules vary state to state so start looking those up.

Note that generally in most states you have to be looking for a new job when receiving unemployment... so keep tose rules in mind.

But you can still use your own time to start a business, although any income from that may impact benefits.

In some states like NJ for example, you can claim unemployment even if you are working as long as you can show that your hours or income was reduced significantly usually by the same employer. Find out in your state.