Running tires beyond (or well beyond) the sidewall pressure rating comes with a variety of failure modes. You never know until it happens, though. In every case, the only remedy is to replace the tire. In my personal experience, here are a few of those failures:
Vee Speedster 27.5 x 1.95 on Velocity Cliffhanger rim. Rated psi: 50. Tested psi: 55. Tire blew off the rim about 1mi into 2nd ride on the tire. It was colder outside than where the tires were pumped, and the brakes hadn't been used, so the tire pressure didn't increase during the ride. The tire got tangled in brake pads and was destroyed.
Continental Gatorskin 700c x 28mm on Velocity Dyad rim. Rated psi: 116. Used psi: 110-125. These tires failed slowly over thousands of miles. The sidewall delaminated from the wire bead.
Panaracer T-Serv 700c x 28mm on Bontrager Clyde rim. Rated psi: 116. Used psi: 110-125. These tires failed after thousands of miles. The wire bead stretched such that the tire would blow off the rim at reasonable pressures.
Panaracer Pasela (various versions) 700c x 32 and 35 on Velocity Dyad rims. Typically used at 0 to 15psi over sidewall rating. We've put many thousands of miles on these tires over the years. Eventually, the sidewall rips away from the bead.
Except for the Vee Speedster, the tires all had been used >2000mi and >2 years at time of failure.