Could a contractor be liable for my vet bills if they let they let the cat out?

I have a contractor who let my cat out while doing work. This was the third time that this contractor was trying to repair the same damage and they didn't find the problem the first 2 times. The contractor was at our house until 11:45 at night taking out damaged walls and it wasn't until the next day that I couldn't find my cat inside. I looked outside and found him hiding in with our outdoor equipment. Fast forward 3 weeks, I have to take him to an emergency clinic due to labored breathing. They do an x-ray and find that he has pyothorax (a chest full of pus). This is condition is most commonly caused from a bite wound. All the vet care is amounting to a little over $4,000 (so far) and the road to recovery could be months. I'm wondering what the liability would be since if they had done their job correctly the first time there would have been no third visit to let the cat out in the first place.