Anecdotally the gyro accidents fall into two distinct categories:
"Early" gyros - gross instability leading to inflight loss of control, in flight break up and other terminal for the machine and almost inevitably fatal for the operator accidents. Total number of accidents / deaths low as gyro was mainly homebuilt, production numbers limited and flight hours low due to reliability but rate per flight / hour / number very high. (numbers stagnated to about 30 ish on the UK reg at any one time...as one was built another crashed.)
"Modern" gyros - mainly factory built and in the UK compliant with / to Section T. Large(ish) numbers. Introduced a whole new group of people to gyro flying as a cool looking crossover between weight-shift micros / helicopters and motorbikes.
Accidents mainly look like rollovers on take-off / landing at low(ish) speed and performance planning resulting in hitting obstacle in take-off path. (short take off but very long clearway needed). Both painful but usually much less fatal for the occupants though it does leave a fair number of written off machines.
In conclusion for a new gyro hull insurance likely to be (relatively) expensive (if available) but much less chance of being dead than in the old ones. I've flown a couple of newer models and I'm a chicken.