The short answer is that it will depend on each program's T&Cs.
Alaska Airlines (and I'm sure others) T&Cs say: "Awards or accrued Miles, including purchased Miles, do not constitute the property of the member to whose Mileage Plan account the miles have been posted". If miles are not "property" then they cannot be passed by a will. Thus after death no one has a right to use them.
If they catch you using someone else's miles in violation of the T&Cs, they might void your tickets/reservation and the remainder of the miles left in the account.
If an airline allows transfers, they might let you pay the appropriate fee to transfer the departed's miles to your own account so you could use them.
If not, I bet even the most cold-hearted airline would let you donate the miles to charity if you ask nicely.