I had top teeth removed for denture. One tooth broke and had to be taken out in pieces. Area is still sore after three weeks and I noticed a piece of tooth still in. There is pain when I try to remove it. Will this piece work its way down and out or no I need to go back and have it removed? If it will come out on its own, approx how long does that take?

Shouldn't you ask the dentist?

You need to go back to the dentist and how you endured for weeks with this issue is beyond me. I would have been back after a day or two.