If they can't produce any or if the income is low I would not rent to them under any circumstances.

IRS require to own the home and used it as your main home during at least 2 of the last 5 years before the date of sale to exclude capital gain up to $ 250k filing single or $ 500k filing married jointly.Under medical reason or change in job circumstances, you can at least exclude partial capital gain of $ 11.5k ish as mentioned by Natalie.

My personal rule is that my lease only changes under a few circumstances. 1) I found something new I want to add because of some new education. 2) My attorney saws something needs to be added or removed to comply with the law or reduce my liability. 3) My tenants have, by their behavior, shown me a short coming in my lease.Here is a little montra to say to yourself "a vacancy is a blessing compared to a bad tenant".

May be different circumstances elsewhere, however.

*There are "extenuating circumstances" exceptions that allow only 3 yrs, but that's only for a divorce, accident, layoff, etc beyond your control and you better be able to document the crap out of the hardship, income loss, dates all match up, etc.I'm not licensed in NY, but if you need a rockstar LO there, PM me and I will connect you.

What would you do in this circumstance?

If you put yourself in their position then you can imagine that they're hopeful that, regardless of their current circumstances, they'll be able to sell for top dollar.

I've seen circumstances where the pastor has rolled up in a Bentley but somehow couldn't pay the mortgage.

Depends on the facts and circumstances that occurred leading up to the disposal.The burden is on the tax payer to show that the property was purchased as an investment (capital gains) versus a business (flipping).  

An HOA lien is not superior to a first mtg, under any circumstances.