Don't do it.

If they don't move out at the agreed upon time, then you have to evict them and that can take ages.

Don't close until they are out.

What you are referring to is called post-closing possession by the seller (here). It is done, but is rare. When I've seen it, there is a lease executed between the parties prior to closing and there is some consideration provided by the seller/tenant to the buyer/landlord, even if that consideration is $10. 30 days is a long time. When I've seen the post closing possession process at work, it is usually for a week or two. There is no question that it is risky as the seller can make it difficult for the buyer to gain access to the property post closing. I've seen it work but it is not common by any means. At least it isn't common here in S Florida.

Ask an attorney what you would need to do to protect yourself if you go down this road.

Edit: When we write those leases for this type of occupancy, there is a huge increase in the rent amount due the buyer/landlord as a penalty if the seller/tenant doesn't vacate by the end date of the lease. For example, lets say you agree to 2 weeks @$10 for the term of two weeks. Beginning day 15 the rent becomes 2 or 3 times whatever the market rent is and also there is an amount held in escrow for damages to the property. Your attorney, along with your agent, can give you examples of what others have done with post-closing possession.

Given what you posted about the sellers other properties, this sounds like a negotiating strategy to me.

Nope nope nope. Red flag says they'll try other hijinks, too. I would not trust them.

Just reply that you'll close in 60 days instead. My guess is they want the closing money but need more time to get their belongings out. Too bad. There's nothing in it for you, so the answer is "nope".

Move the closing out 30 days to their target transfer date. Possession at time of closing. That is the most simple solution.

You don't know these people. You don't understand their motives. They may need the extra 30 days and have a good reason. But, it isn't your problem. Before you entertain a 30 day possession after closing, why don't you ask them why the need such an unusual accommodation? Then, you can make a judgement as to whether you want to entertain the proposition.

There are good reasons why you would have an occupancy after closing. I've done it twice. In both cases the buyer approached me to buy my property without the property being listed for sale. In both cases, I needed time to find a property to buy and to go through the closing process myself. That was a legitimate reason for an accommodation.

Neither buyer needed to move in the day after closing. I have to emphasize that is an unusual circumstance. Unusual circumstances do happen. Just be very careful to protect yourself and your interests.

I can't believe the nerve of asking for no rent, leaving you to pay the mortgage, taxes and insurance for their free ride. I can't think of any possible or reasonable answer for that request.

First off, your sister is one smart cookie. Listen to her.

Are they saying they want to stay for 30 days AFTER closing? Or do they want a closing in 30 days at which time they will leave? No to the former, yes to the latter. See https://www.houzz.com/discussions/5778650/sellers-not-out-of-house-at-agreed-time#n=9

30 days of free living is 30 days of FREE. I wouldn't do it for all the reasons mentioned above.

If the terms are not good for you, counter with terms acceptable to you. Keep the negotiations moving with acceptable terms.

Hopefully you have proceeded with the negotiations and reached an agreement.

I had to ask for after sale tenancy, only because the closing was postponed, and postponed again, due to issues with their financing - with little communication to me. Consequently I lost the rental that I was going to move to (until I was ready to move out of state) because I absolutely could not pay both rent and mortgage & utilities. I made a fuss so they agreed -- but we did have a written agreement, and I paid rent to them.

The only problem that I had with it is, again, with no communication, they tried to flip the property and would come in to show it (this was during the real estate craze in the late 90s); I would have strangers knocking at the door wanting to see the property also. I hadn't realized that the agent and the buyer were in cahoots and speculating in that RE boom.

That was an odd circumstance that isn't too likely to happen again (to anyone, I hope!)

raee_gw, I'm so sorry you had to experience that awful sale. It sounds like your agent didn't do proper due diligence on the buyers lender before presenting the offer to you. And to have the buyer and their agent speculate on the RE boom without first informing you is an ethical violation IMO. Nothing wrong with speculation, but when it interferes in the sale like your purchasers did, then it's a problem. Fortunately you closed.