There are people out there far more knowledgable than I but my understanding is that anyone can sue anyone else for any wrong done. Whether they succeed is another question.
However if you pay a landowner to access his land then he has a duty of care to prevent stuff happening like removing broken glass, barbed wire etc. (for instance I have to prevent access to my climbing tower by means of padlocked wooden boards and warning signs, even though it is on a private site. However, if an idiot chooses to ignore these deterrents, climb up and then fall off I will have done all that is reasonable to prevent harm and it's tough on the idiot.)
If you have an accident with a commercial group whilst caving and you are negligent, then you are liable (i.e. you don't protect an obvious drop with a rope etc.) If the negligence is shared, the liability is shared also. The commercial centre will get sued first, then their insurers may sue the landowner if there is a possibility of shared liability and the landowner made a contributing factor. But simply paying to access the cave / land does NOT make a landowner automatically liable for an accident in the cave.
Like I say, I'm not an expert but in my experience this is what happens. I'm sure it can be much more complicated, though.