I had a tag stolen off my pickup at a motel in Reno. I was moving there, so I just called the issuing state to report it and then got Nevada tags. My first visit to a Pep Boys was for anti-theft license plate hardware, stainless steel screws with tamper-proof Allen heads. I can't remember if they came with nuts on the back or if I added those for good measure.
Maybe not as much with trailer tags, but I think stolen license plates often involve another crime. Fake tags on a getaway car, for example, or fake tags on a stolen car. I think a person should expect to get pulled over if their vehicle and plates don't match, especially with plate readers.