IF batter successfully bunts, runner is usually safe at home. BUT, if bunt pops up, runner is dead. Or obviously if contact isn't made (missed bunt attempt or missed signal), runner is usually dead.

Our pitchers were told to "stick it in his ear". a batter will usually bail if a ball is coming at his head. Result is usually an out for the runner on third, or at least a retreat back to 3rd base. Of course no a good idea when bases loaded and three balls on the batter.

Then there's a safety squeeze, where runner doesn't go until contact is made.