Unsure if I am responsible for damage! [USA]

I recently stayed at a cabin. After 4 days, I received a message saying one of the legs has slightly come off from a chair located in one of the lower floors of the house. During my stay, I only used the chair to place a small bag on it occasionally (10 pounds max). It was in a room that was rarely used. I never sat on the chair or caused any significant stress to it. It didn't topple over when I left or showed signs of damage, so I'm unsure how I was supposed to catch that I had somehow broke it.  I'm unsure what to do because they want me to replace the chair for $130.

Without prior notice that the chair was fragile or should be avoided, I used it as one would reasonably expect of a chair. If the chair was already in poor condition or had existing issues, it’s hard for me to believe that I should be held responsible for damage that was caused by normal, intended uses. I'm afraid it's seen some wear and tear from previous guests and maybe gave out when I was there. I am unsure how to handle this situation.