Some thoughts on this in the case of the latter, ...

establish a channel that sends 1 sat per day to the remote.

if the local balance of the channel is depleted, consider the operator dead.

An operator can replenish the local side of the channel by a rebalance.

maybe this channel type makes sense to be an issued asset, unique to that channel. Value is still conveyed through sats, but there needs to be certainty that only authorized end nodes can push value to replenish the balance. Or perhaps a private channel would suffice if the remote side is involved in the annuity administration?