The rules do cover running out of waste: you can still do things that would normally cause you to take waste cards, but you can ignore that part of the action.
Rules p6 wrote:
... If some of the card’s effects cannot be applied, you cannot apply any of the effects. There is a single exception to this rule, in that if a card requires that you gain Waste, and there are no Waste cards left in the Waste deck, you may still apply the other effects.and
Rules p9 wrote:
This means you have to take a Waste card from the Supply and place it into your “gained cards” area. Waste cards are a burden. You can’t do anything with them and they take up space in your deck. If there are no more Waste cards in the Supply, you do not have to take a Waste card. [underline added]