Since the rules vary depending on which lottery you are interested in, and which state's laws apply in the state you live in, it is pointless to solicit speculation from the general Internet population. Instead, look up the *actual* rules on the appropriate website.
Here are the Powerball rules for New Mexico from
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"A Lottery prize is like any other asset. Per the New Mexico Lottery Act, prizes may be paid to a deceased winner's estate or to a person designated by judicial order. In the event of the death of a Lottery winner during the annuity payment period for the Powerball, Mega Millions or Hot Lotto game, the remaining annuity payments may be paid each year to the estate. Or, upon the petition of the estate to the New Mexico Lottery, with the approval of the Multi-State Lottery Association (MUSL), the Lottery may accelerate the payment of all the remaining Lottery proceeds to the Estate. If such a determination is made, the cash value of the securities and/or cash held to fund the deceased Lottery winner's annuitized prize may be distributed to the estate."