If I were in your shoes, I definitely wouldn't want to come up with the dime for paying on something like this.

So, my guess would be that they already owe their current landlord rent, and they're hoping to get away with some free rent from you before you kick them out.I'm not in your shoes, so it's easy for me to tell you to just not rent to anyone who doesn't meet your normal criteria, which I hope is normally really tough. 

If I were in the OPs shoes, I would first, check with my lender to see if what the seller is proposing is legal  (my guess is no) .... then, once I purchase the property i would ask the tenant to fill out an application and go from there....then join your local rental property owners association, take a new landlord boot camp class and use their forms so you can be sure to have the correct forms for your locale  oh and also read the local landlord/tenant laws  

How would you react if you were in their shoes?

But not likely.If I were in your shoes, I'd spend the next 12-24 months aggressively paying down debt and piling up cash once you're done with that. 

If I’m in your shoes I’m probably going the condo route, the biggest targets for you right now should be subsidizing your housing costs as much as you can and safety.

That is, say they need a wheelchair, you can accomodate them by allowing them to install their own ramp, but you aren't necessarily required to build it yourself.Might be wise to brush up on the Fair Housing Act and chat with a lawyer to understand the nuances in your particular area.If I was in your shoes, I'd ask: "Are there any legitimate reasons I might not want to rent to this person (credit, evictions, felony, etc...)"

@Jean SooI was in your shoes recently w purchasing a house this year in March and had to rent it out in April.

What would you do in my shoes where I'm essentially putting my home on the line in the midst of this? 

I just recently attended a three day weekend in Dallas I always go to these things waiting for the other shoe to drop.