First, what do you mean by "finished"?
Is your annuity currently providing income to you, or is it in the deferral period before income payments begin?
In either case, an annuity is a contract between you and an insurance company.
The contract will state--very clearly--when the deferral period ends or when annuity payments end (in the event that there is a limit on the amount of time or "term" that payments are made).