I know of a couple banks that do what is called asset depletion.

You should also require this information is updated annually.You can still place reasonable restrictions on the animal, such as: Requiring a current (and annually updated) Veterinarian report on the health of the animal, including vaccine status; current appropriate local licensing of the animal if required in your jurisdiction; require the animal be spayed or neutered unless contraindicated by the Veterinarian; require the animal to be in a carrier or on a leash when in common areas of Multi-Family properties, particularly elevators or hallways and stairwells; require tenants to clean up after the animal in common areas and/or within their unit, and prevent offensive odors from emanating from their unit; aggressive or nuisance animals (includes frequent barking that is NOT an alert by the animal) can be cause for removal of the animal and/or eviction of the tenants.

Take garbage bags and lots of old towels because oil tanks are never " empty"  In this situation, I'd probably opt to hold-back funds in escrow to pay for a "professional" to remove the tank, perform any cleanup and "certify" all is good (making the lender happy).  

I agree with Jimmy Klein. as a landlord I haven't had this issue. but as a commercial hvac contractor I have had issues with pipes bursting etc. you don't offer the tenant anything. immediately file a claim with your insurance company. hire a remediation crew to clean. up any if the water/ damage that occurred.

Based on the extra explanation, an asset depletion loan may work. 

Possibly you could use that as leverage to make the seller remove the tank and handle the clean up. 

When I turn over the unit, I will just clean up the yard prior to showing.

I also can't charge the tenant that started the problem because their on welfare with no money and I have depleted her security deposit of 750$ from other damages.

I have actually closed on a few of my deals and done some clean-up before putting it out to other cash buyers.

Once bought then how to clean up such a park and convert POH to TOW (tenant owned) is the business model.The hard part (ignoring the huge problem of cleaning up such a park) is getting the seller to accept an offer calculated as:Number of paying pads x 12 x $equiv lot rent from surrounding parks x 0.5 (50% expense ratio) / 0.1 (or higher) for 10% cap rateAdd in nominal value of the homes, $3k for old homes on up a bit.