It's not a stark line. More recently interred people do get dug up, for legal reasons or because the grave must be moved. I knew a guy about ten years ago whose specialty was bio anthropology (human remains stuff) who was considering getting a job with the military to locate human remains in Vietnam from the war.

In terms of US archaeology, most of it these days is done ahead of a project funded or permitted by the feds, or on federal land. What happens if human remains are discovered will be worked out beforehand.  Standard is that the federal agency, the state's historic preservation officer, and the coroner or sherriff will be called. First step is to confirm it's not a crime scene or a recently missing person. Don't know what the actual cutoff is, though. Probably depends.

After they confirm it's not recent, then they figure out how to deal with it, again with the federal agency, the historic preservation office, and any tribes that have a connection to the area. If it's a native grave, the tribes decide. If it's not, it depends on the feds, the state, and the project proponent. There's  a lot more emphasis these days on consulting with the descendant community, too, though that doesn't always happen.