I have a plug inserted while I am lying on a bed, this keeps a sedative suppository in, though I have walked around with it in, I prefer to keep still until my Aunt removes it. It might fall out if I went outside, though the plug shape is like a round bulb attached to a flat base via a narrow neck, I think this is what keep it in place. I recently saw my Aunt insert a plug into another person, and it was quite an effort until the narrow neck went in. I don't think this particular type would fall out. Being glass this plug is firm, but feels cold to begin with and seems to stick in place . Pulling out takes some effort, so I think it is reasonably safe. This Lovehoney plug is very similar:
The ones my aunt have are quite old medical ones.