I'm not sure who is taking the pet right now but there hasn't been any pet damage.

They are backing out on a legally binding contract, causing damage to your business, and it's reasonable for you to recoup a portion of the loss.

I just want to be able to protect myself from damages while it's still learning to be this way. 

So I'm worried if they pull out, aside from being stuck with paying for all the damaged stuff, I may have the city say other stuff doesn't work or wasn't done right by the contractor. 

Long term - it's almost impossible to properly charge the right person for damage to the common areas.

I would say the catch is to understand what caused the damage.  

if it is damaged, an acv policy will probably give you half of the cost to replace.

Enough elementary economics, another true saying, "poor people have poor ways" being poor is often the result of the ways selected to achieve something, slapping tar on a roof when it should be repaired,  later water damage causes a greater loss and the roof still needs repaired. ( "A stitch in time saves nine" comes to mind as well).  

The few circumstances where it would be returned would be for Title issues or damage to the property after your contract was ratified.  

If you want to be looked at as a pro...dress the part.