If you have a lifetime income annuity, the payments will stop when you die, unless you have some other guarantees in your contract (such as the guarantee to at least get your premium back, or receive payments for x number of years). This type of annuity is guaranteed to provide a set income stream for life, no matter how long you live. So you may end up getting a slightly reduced interest rate if you opt for those secondary guarantees.
If you have an annuity that is set up to pay out for a certain number of years, and you died before those years were up, the remainder of the annuity will be paid out to the beneficiary you named on the contract.
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If you have an annuity that is set up to pay out for a certain number of years, and you died before those years were up, the remainder of the annuity will be paid out to the beneficiary you named on the contract.