If the one person wants to stay, then tell her the terms of the lease and give her a deadline. 

An attorney can ensure your contract has the deadlines and can answer questions like, "Where do I put the earnest money deposit?" 

You miss a deadline and then you have to let them stay longer.

One option is to tell them you won't require them to clean but you'll still give them a full refund of the deposit if they are out by the deadline and there's no damages.

Then give them a deadline.

Not doing a bad deal is MUCH better than doing any deal just to get your feet wet or meet some arbitrary deadline (which is, at the very least, stupid and likely a prescription for disaster). 

There is an offer deadline of highest and best due by noon tomorrow.

Hi Duncan, Yes you can negotiate during the due diligence stage and you can try to negotiate at any point in the sale process until close.If you end up not being able to move forward during your due diligence, your earnest money deposit should actually be fully refunded to you, provided you put in the contract that your offer is contingent on your ability to do your due diligence.There were several deals I worked on where additional repairs were found during our due diligence that necessitated negotiation.What we did was thoroughly explain to the seller the impact of the additional expense and then offer them the options of moving forward at a lower purchase price, or working out terms at the same price (owner financing/sub2/something else), or cancelling the agreement.Usually, the seller would choose to move forward at a lower purchase price but we definitely had parties choose to cancel or finance too.If they chose to move forward at a lower purchase price, we'd write up a simple 1-sentence addendum to the original contract stating the new purchase price and have both parties sign.You may want to include a deadline in writing of when the seller must respond by before you move forward with cancellation so you don't lose your EMD.

When you need the tenant to take action, always include a deadline and a consequence for failing to perform.

Nathan is right, tell her you need proof that she's applied and then fill out the other form and give her a deadline.