Imagine what an object would look like teetering on that limit, a tiny mote of frozen hydrogen touches down, and now it's over the max, and FOOOOOOOOP the inwards collapse begins...
For white dwarfs, at least, this process is one possible way to trigger a supernova--a white dwarf right at the limit accretes some more mass and collapses catastrophically; the collapse triggers a supernova explosion.
