Insurable and assignable are two different things. An insurance policy will normally not cover the tortfeasor (the party that commits the tort). The person who would want to assign their rights would normally be the one who was harmed, not the one committing the harm.
Whether a closely held corporation could assign its claim to a shareholder will depend on the circumstances and the type of tort. In most cases I wouldn't expect that there would be a reason for the corp to assign the claim, but instead would expect the corp to pursue the claim in it's own name.