Why would a gyro abruptly stop? If there's some sort of collision with enough force to crumple the gyro casing, which appears to be buried deep in the vehicle and can be made of very strong material, you have a lot bigger problems than the gyros stopping.
Still if the traction system in cars fails you dont fall over and and lie on the street immobile. They have a second one for fail safety, but i think there could relatively easily be a case where both fail, like no energy for whatever reason.
Gyros spin very fast on very efficient bearings. A rotating mass will not stop immediately unless forced to do so. So even when power fails completely, the gyro will continue to rotate for quite some time (several minutes probably) and fulfill it's purpose - well, unless something penetrates the gyro housing and blocks the spinning wheel. But then I guess your problem is not limited to falling over.
Another issue with fast spinning disks is that they can rupture and send splinters flying, but it's rather unlikely that both gyros fail in the same catastrophic way at the same time.
It does not appear to me that the second gyro is intended to add reliability. Watch how the gyros move in the video: the rotors rotate in opposite directions and the frames twist in opposite directions to apply force to the vehicle chassis. That is necessary so that vehicle pitch motion is not coupled into vehicle roll motion by the gyro. So if one gyro were to fail, the vehicle would rock side-to-side every time it went over a speedbump.
I didn't downvote you, but it is physically impossible for spinning gyros, with their massive angular momentum, to suddenly stop without a sudden massive impulse of countervailing torque. Barring catastrophic (i.e. the driver is already dead) damage to the vehicle, there is no mechanism that can apply such torque.
(edit) OK, let's make "abruptly" optional. So what's the contingency plan for when gyros spin down and stop?