Usually price.If the absorption rate is pretty low, you'll want to react quickly so you're not accruing empty days on market.

I would also make sure that the current owner transfers the deposit along with accrued interest.

Typical items that fall into that category include"Mortgage interest that accrues between closing date and month-endReal estate taxes paid into an escrow accountThey are typically paid at closing and rolled into your final loan amount.

I tell them rent will continue to accrue until/unless they PROPERLY surrender possession.  

Is the Contractor not doing his due diligence by not doing this, and what type of risks are they accruing by not doing this?

I would like to flip homes at this point in my life, and accrue enough capital to purchase and hold investment properties to help my retirement.

You will have tax benefits and accrued equity though.

Sounds insane, I know, but cash flow is a huge issue here, and we're working on the assumption that when she passes there will be no estate to pay the debts, so the amount of interest accrued is somewhat irrelevant.

IF your child wants a career from a college education, perhaps the accrued RE's cash flow could pay the college bill and remain long after. 

It will long remain the mystery why if, for example, I don't pay my own water bill the service is stopped but other accounts are left for a year or more to accrue charges without being shut off.Our company asks in our management agreement whether you would like us to handle water/sewer billing.