Can a tenant be sued SUCCESSFULLY for loss of income if they left behind damage that requires time and money to repair and prevents the apartment from being rented to new tenants?

I had remodeled their unit to repair pet damage from past renters, as well as I remodeled my unit for the same reasons, therefore I chose not to allow pets.

Later in the evening we went over with fans and took photos of the visual damage.

In both, you should first document the damages and attempt to send the tenant a list of monies owed. 

The fire dept turned off the water at the street by the time our guy got there, and the City quickly got involved exerting a fair amount of pressure.In the interests of keeping this story short, these are all the things that we had to do: Communicate with the property owner, the tenants, and the city constantly, offer hotel rooms to affected tenants (some took us up on this), secure the building from future squatters, get the water main and all pipes thawed out, have the water company turn the water on at the street, have a crew of plumbers isolate and repair/replace broken pipes in a muddy crawl space, clean up the mess created by the water in the basement/crawl space, get into all apartments to inspect for damage, test and get water service restored, and repair some internal damage to one of the apartments (that's still in progress), and apologize to the tenants. 

Being so close to the house I want to take care of asap to avoid damage to the foundation.

There were no signs of water damage anywhere and it's one of the cleanest unfinished basements I've been in. 

Couple that with the housing shortage due to hurricane damage we have in this area and the skyrocketing cost of housing, and there couldn't be a better time to list a vacant duplex-If you have equity in the property as it sits, and you're creditworthy while she isn't, now is also a great time to start a new investment with your equity from the sale and move on without the added difficultiesManaging a property yourself is already hard.

This eventually leaked into my bottom unit .Ceiling has obvious damage with water lines and traveled to my hardwood floors and it’s surrounding perimeter .

Both toilets are independent until the pipes meet, the damage can be only on one of them.