I thought there already was a West Virginia Cave Law and, yes, there is. The NSS has it posted under conservation with all the other cave laws. Here is what it says about liability:
(a) Neither the owner of a cave nor his authorized agents acting within the scope of their authority are liable for injuries sustained by any person using such features for recreational or scientific purpose if the prior consent of the owner has been obtained and if no charge has been made for the use of such features.
The question of liability seems to be open in cases where prior consent has not been obtained. The Virginia Cave Law has similar wording, but does not mention prior consent.