Torn out drywall, open bags of garbage festering on the floor, several mattresses and soiled furniture piled up on the porch and in the living room.

So if you shop well ahead of your sale so you've got the market where you're looking nailed cold. 

I shopped specifically for brokerage firms that have a property management branch.

It simply needs to be already rehabbed and also rented out.So shop around on your banks.

We've have had similar problems with both pets and garbage (apparently the garbage bin, at the side of the building,  is "too far" of a walk, so they leave bags on the fire escape for the raccoons and crows to rip open and shower down on the neighbourhood).We first sent a letter to all tenants reminding them of their obligations for their pets, pets belonging to their guests, and their garbage.When that didn't work, we sent another letter proclaiming our disappointment and the actions we were going to take to remedy the situation ... namely hire someone to pick-up the dog faeces and garbage and to ensure the garbage is put curb-side for pickup on garbage day each week.  

@Stanley CrawfordFirst, there're LOTS of people who miss depreciation, and unfortunately even CPAs miss it, not to mention the franchise shops like H&R Block.

I also leave a “welcome basket” containing about $20 worth of goodies including dark chocolate, good ground coffee, a bag of popcorn and 2 bottles of water.

One could say that should have been more aggressive in shopping and tried to buy a $120,000 house at $100,000 (e.g. by flyering or something).But here-in is the problem.

Check the forums on the topic - basically shop for rates and max duration.

I shopped around a fair bit, but was mostly calling local/regional banks, who all gave me the same answer.