In the rivet's frame, "the end of the rivet hits the bottom of the hole before the head of the rivet hits the wall" - the bug is squashed. In the bug's frame, "the rivet head hits the wall when the rivet end is just 0.35 cm down in the hole" - the bug remains alive.
Needless to say, the bug being squashed in the rivet's frame and alive in the bug's frame is fatal for special relativity so Einsteinians resort to an idiotic ad hoc "requirement" - the rivet shank length miraculously increases beyond its at-rest length and poor bug gets squashed in both frames, Divine Einstein, yes we all believe in relativity, relativity, relativity:
Yet even the idiotic length-elongation requirement does not save special relativity. As judged from the bug's frame, when the head of the rivet hits the wall, an enormous stretching force will separate head and shank, that is, the rivet will be broken. The bug will be squashed by a headless shank.
This "enormous stretching force" is absent as judged from the rivet's frame, and the bug is squashed by an undivided rivet.
The contradiction is even more clearly seen in the pole-barn scenario:
If the pole is replaced by a rivet whose head cannot pass through the door, then we have head-shank separation as judged from the barn's frame and no separation as judged from the rivet's (pole's) frame. Reductio ad absurdum par excellence. One of Einstein's 1905 two postulates is false.