The bindingness of promises after the death of the promisee is debated by philosophers, mainly I think because of the intuition that one can't owe anything to someone who doesn't exist (if I promise something to the Tooth Fairy, I don't need to keep to it). But in fact it seems quite obvious that it is possible to be bound by a promise to someone who doesn't presently exist. Sam is about to go on a trip, traveling until the beginning of next month. He has me promise to take care of his pet rat until his return. It surely does not matter for the bindingness of my promise whether Sam is planning on traveling by car, plane, donkey cart... or time-machine. But if he travels by time-machine to the beginning of next month, then as soon as he has departed it will be true to say that he doesn't presently exist. Yet, surely, he will be right to blame me for breaking my promise if five minutes after his departure I let his rat out to be eaten by the cats, possums and maybe snakes that roam our neighborhood.
If time travel is impossible, I can run the argument with gappy existence. Maybe you don't exist when frozen. Sam has himself frozen until next month. Etc.
Still, the idea that one can't owe something to someone who doesn't exist is plausible. If we are eternalists, we simply say that this principle holds when we talk about existence simpliciter, but not when we talk about present existence. Promises to those who currently don't exist may, however, make trouble for presentists.