So as the post says, this rental stinks after tenants moved. Has anyone dealt with this, and remedies please, I did allow 2 pets. 

They make some great products to essentially seal off bad odors like smoke and pet and we have been in some incredibly bad pet odor damaged homes! 

As you begin the drying process, you may inadvertently cause the mold to "bloom" and become active as you lower the water activity levels.The musty mold odor you are familiar with and do not smell in this basement is known as "MVOC" or microbial volatile organic compounds.

There wasn't residue, lasting odor, etc. so I don't believe it was ongoing.  

AndreaAndrea Short,Can you smell the odor of Tampa Electricity in your area?

I use Concrobium from Lowes because it seems to work and doesn't have an off-putting odor.

Pictures are shown below but the one thing that is missing from the photos is the putrid smell of cat urine and feces (along with other odors too).  

Contact a local odor removal service and have them come over to analyze and recommend the best method for remediation.

You are responsible for the safety and health issues in your building, and hoarding and odors like you describe are health issues (think rats) for the entire building. 

I'd like to avoid anything that would make it unpleasant to live there (odors, damage) whereas we're fine with "preference" items like countertops, flooring, paint.