Overflow incontinence happens when your bladder gets so full that the sphincters physically give way and you pee yourself. In other words the muscle would give before the bladder ruptures. I came across a thread about Tycho’s death on Reddit and virtually no one was calling bullshit on the story that he died of a burst bladder because he was embarrassed to go to the bathroom during a banquet.
The first thing that comes to mind here are prostata problems or kidney stones. While the ring muscles can’t counter the pressure from a full bladder, the other two can seriously obstruct the urinary tract. In case of a kidney stone, it could even be that sharp crystals support or cause a rupture.