Not a good idea, IMO.Won't that require a tenant to have a bank checking account, some older people just use cash still and have a savings account like a little old lady I had who didn't trust banks (actually she was correct..LOL)

I'd rather risk essientially lending good people $300 (if I can afford it) in their time of need and feel good about myself than risk losing them, by forcing them into a move that will cost more than rent and force a lady and husband with a broken arm to move a bunch of boxes and furniture. 

When you do get in contact with the lady, if she is full of stories and excuses, just simply refer her to the lease and the laws.

If the lady qualifies on her own, why not rent to her?  

She seemed like a nice lady, like a grandmother.

My property manager rented the place to an elderly lady who appears to be suffering from dementia but is assisted by her daughter.  

The lady is currently paying $1340 where she is and they are increasing the rent to $1650.  

She is on a month to month lease and my wife is to the point where she wants this lady given 30 days notice and gone as part of the sale. 

Even though this lady is nice and pays on time and, it's hard to find people like that, she's got her bad side which is going hard on the house.

Of course if they were not willing to then work with me that would be another story but it seems like this lady in your situation is trying really hard to keep her home, but in the end it is entirely your call and your budget and what it can sustain.