I have to assume that you don't live in the US. The license plate can't always follow the car: each state has its own license plate(s) and DMV and rules, etc. e.g., I got a nastygram from New York state when I moved out of state and didn't turn in my plates. OTOH, in Minnesota, they tell you to do whatever you want with them: turn them in, throw them out in the recycling, etc. Some people have license plate collections on their garage walls.

If a license is stolen, You need to go into the DMV because they'll have to take a new photo. There was a temporary exception due to COVID, but I think that's no longer available since I had to go into the office when my license expired.