My current lease term duration states it shall start from XXX to and including XXX. 

This house offers convenient access to XXX University (10 mins), XXX Hospital (5 mins) and lots of shopping including Costco, Bed Bath & Beyond, Petsmart, Kroger & more just minutes away.

Anyway, I overheard her say something like "$xxx a month, like, I can afford that" (in a 'who couldn't afford that' kind of way).

That is the value of appreciation speculation over  renting it out and losing XXX per month, sleepless nights and possibly have the house destroyed by tenants.

Consider getting a holding deposit in the future.Receipt is hereby acknowledged of one hundred fifty dollars ($150.00) Holding Deposit from xxx (Applicant) to hold the rental unit at the following address: xxx until xxx.If the unit is not available at the agreed upon date the landlord will make a full refund of the deposit without interest, and with no liability or penalty to either party.

It is in the very desirable area of xxx.

At the end of the day, you need to tell them, "The rent is paid by XXX.

What I'd do is put a clause that is very clear and specific:  Renter's insurance is required with continual coverage during the tenancy that covers (put your requirements here - liability in the amount of xxx, loss of use in the amount of xxx, etc.).  

So, you'd write a check for $XXX made out to "John Doe and Jane Doe." 

If a section 8 is approved for XXX and agrees to rent a unit for XXX + X by lying to their handler that is not the landlords problem.