If the primary owner is involved in an accident can the cosigner be held liable for personal or property damage?

I am not an attorney but to my understanding, yes they can!! The other party just has to prove your At Fault. For instance, you co-signed which allowed the primary to get the vehicle which did the damage without you the primary couldn't of gotten the loan and therefore it is your fault. The only way you might not be at fault is if you are not named as a registered owner of the vehicle.