Unfortunately with those numbers it's tough to find a non-bank lender/financial institution that will lend.Usually loan minimums are $50K and the up to 75% LTV on purchase-money/70% LTV on cash-out refinancing, which basically means you need up 25-30% depending on the type of financing. 

Zillow seems to do minimal verification of information provided and that just isn't good enough.Your situation does seem strange though. 

What would you do in this specific situation?

If you need financial help, ask under the "Finance, Tax, and Legal" forum.

This gives you a foothold in the market without overextending financially, and you can always explore other investments later.If you can find a multifamily property in Asheville, that’s an even better house hack.

Also, consider this copy & paste advice below:Recommend you first figure out the property Class you want to invest in, THEN figure out the corresponding location to invest in.Property Class will typically dictate the Class of tenant you get, which greatly IMPACTS rental income stability and property maintenance/damage by tenants.If you apply Class A assumptions to a Class B or C purchase, your expectations won’t be met and it may be a financial disaster.If you buy/renovate a Class A property in Class D area, what quality of tenant will you get?

It could impact your home equity and financial security.For a safer and more specialized alternative, consider a Fix & Flip loan. 

I’m also considering advising my tenant to look into Section 8 assistance, as it could help support their financial situation while allowing me to adjust the rent closer to market levels.

They will pull a personal background report, will check IDs and question your current living situation.

Don't get me wrong, there are plenty of terrible landlords out there, but deciding that you are victim of life's circumstances certainly won't improve your situation.