Following is a list of the clauses I have included in my contract to deal with the more pesky creative problems clients have come up with through the years. You let my cat Fluffy out of the house, and I can't find her. You are dead meat. You'll pay for this. If Fluffy is missing or in kitty heaven, this is no idle threat.
Homeowners can become understandably furious if something happens to their favorite pet.
The legal threat, however, is minimal. Actual damages are limited and hard to evaluate. Do not underestimate the emotional angst. This kind of thing can terminate the relationship, even if things were perking along just fine. It is the owner's responsibility to make sure pets are secured throughout the construction period.