What happens to the unspent resources in their resource pools? I cannot find any explicit statement about this in the rulebook.

Resources are gone.

I haven't found anything in the rules either, but when I play, I put the resources back in the resource token pile (actually I have a little plastic tub). My reasoning behind this is that if the hero dies you lose any attachments that were attached to it so you should lose the resources too.

I would agree. Resources belong to your individual heroes - they don't share them with the rest of your team. Anything that belongs to those heroes would be put out of play or discarded. As of right now the only way to transfer resources from one hero to another is the Leadership card Parting Gifts.

Resources and everything else on the hero are discarded when a hero dies. That is why they created Parting Gift.

silverhand77 said:

I agree to this reasoning. Next to that, FFG spoilered an objective card for the next AP, which also gets resource tokens placed on it. If you knew the card text (I don't want to spoiler it here in case you don't), you'd agree that it assumes that the resource tokens are automatically removed when this card leaves play again, otherwise this objective card wouldn't make sense. So I assume whenever any card leaves play, any tokens or attachments of it are usually discarded.