Does being std::move'd affect references?

I'm trying to make sense of some code I'm looking at, and one thing that I noticed is that one class keeps a reference to this one object in a reference member, while some other code move constructs it.

I'm curious how those play together. Is a reference member still valid if the underlying object is the source (or target) of a std::move operation?

How about if I happen to know that the underlying object has all its move operators custom defined to just std::move all its members? Presumably in that case the reference to it is valid when the source object being referenced is valid, and not valid when it isn't, right?