I don’t think they exist any more, but in some old movies, and I recall in an episode of Dragnet, hotels had “house detectives.” The implication was that they were there to prevent the hotel for being used for prostitution, but that was never stated clearly, and sometimes you get the impression they’re there to watch for adultery. No mention or implication of their being there to protect the guests from theft.
This was asked recently. The brief answer is that their function is now taken over by hotel security.
They also may have looked into making sure only married couples shared rooms, but probably didn’t get involved unless there were other problems.