I'm guessing the property has been neglected. if they are unwilling to fix,  negotiating an amount off the purchase price will help as well.

Unfortunately, they were unwilling to come to terms on a price. 

If you're unwilling to comply with my policy, then I'm sorry to say you won't be able to rent from me."

So some sellers are unwilling to play that game and will only consider buyers that have "funds in hand".

When things get worse and the government is unable or unwilling to keep pumping out cash.Like the fabled grasshopper, you are dancing in the fields enjoying the sunshine and we wise ants are toiling away... because winter is coming.

It doesn’t mean that your agents bad or unwilling to do the extra work.

The options then are these if they are unwilling to put it on the market:1) stay and refinance - they dont have the credit or income to qualify for a refinance, they have tried and were denied.2) they sell for $580k - if they do this, they will receive about 200k after paying their current mortgage off

You also cannot refuse to rent to a tenant because they have kids and you're unwilling to test and remediate. 

Now the new owner is unwilling. 

When dealing with traditional sellers on these types of properties you typically have an option to cancel if the property fails to appraise, especially when financing, that forces the seller to return any EMD monies if they are unwilling to accept the lower price and you cancel the contract.