When I first started working at my current store it was part of my job to clear such damaged items off the shelf before the customers encountered them. So yes, I’ve seen plenty of stuff with broken tamper-seals. It wasn’t a constant problem but it does happen.
Yeah. People do that - take a swig of mouthwash (or other stuff). Take band-aids, or OTC pills, and for awhile we had someone who would still just one eggroll out of a package in the freezer section and leave the rest.