For us, if anyone uses the night drop regularly they must sign an agreement, whether or not they have a key. And while our agreement doesn't list out each signer, whoever signs the agreement is agreeing that only those listed on the signature card are allowed to deposit bags/envelopes, and "perform any act with respect thereto as he or she may deem proper."
Honestly, we are small and most of our change orders come from the same places and the same people, and I haven't dealt with a situation where customers put money in the night drop for a change order the next day (or whenever). Usually whomever is picking up a change order will have a check or cash with them and we don't make them sign a receipt. If everything checks out alright, we send them on their way.
I would say perhaps it might be wise to document ID when someone comes to pick up a change order that was created off funds left in a night drop bag. At least then if something happened you'd have more to go off of than just a signature.