No, there are well-defined procedures for searches that turn out to uncover privileged materials, too. If you think about it, this issue must come up all the time, in all kinds of searches.
A Google search will rapidly avail here, including DOJ's own handbook for how to handle this situation. It comes up a lot!
The problem here is "turn out to". Documents in a safe deposit box might well be privileged but not in an obvious way because nobody expects their safe deposit boxes to be searched by the FBI. The FBI may have seized privileged documents without realizing it.
A Google search will rapidly avail here, including DOJ's own handbook for how to handle this situation. It comes up a lot!