Another option is this: what you can do is take a deposit to hold the place (and have a signed deposit to hold agreement), but they forfeit the deposit if they fail to rent.

@Brandon Carlson no deposit? 

Maybe they really want to move into a SFH and they need a larger deposit to do so, you could trade some cash for those keys in that manner....You also mentioned that the rent was below market, if they are on a month to month lease, then you should be able to start systematically raising rent to bring them up to market. 

I uploaded a pet addendum to apartments.com, asking her to fill out, along with a pet deposit.  

I have a set deposit go in every two weeks and have that investing into a mix of stocks and bonds.

Not only that but you can automatically screen tenants with an application and credit and background checks, collect rent through the app that will automatically be deposited into your account, automate late fees, itll send emails to your tenants when their lease needs to be renewed or when there rent is due soon/late, it'll automatically generate profit and loss statements and tax documents and more!

They moved in on November 15th so I have recieved $2,000 (deposit) and $800 (prorated rent). 

I'm assuming you want to grow your portfolio.....don't start off by on the wrong foot with a Housing Authority. 2)   Get as large of a security deposit as possible.    

My rentals(6 doors across 2 properties) have a bank account for Sec deposits and then an operating account.

@Cathy MalmroseAll else aside, your son is essentially a landlord for this time and he could put together a lease agreement immediately (ideally with the help of an attorney), which outlines a security deposit in case of damages, requires the prior owner to obtain renters insurance, who pays utilities and any daily rent- especially a daily amount that’s high if they stay beyond a certain date.This would at least cover the primary points in a leaseback.I’m curious about when and how the sellers made the request to stay past closing that your son agreed to - was it just between the two parties or was the Realtor part of that conversation?