So if I was dealing with a seller who was insisting on handling the transfer this way, I would be wondering what the seller is trying to hide... and I would figure it out.

If you still have the appraisal and it is completed by an AMC you can transfer it and still close on it.

Your estate could still go through probate to determine how the LLC and other assets are distributed.You may be able to record a "transfer on death" deed for your property so it automatically transfers to another person when you die.

But with the EOY right around the corner need something more reliable. 

@Chris Rendall couple comments,@Wayne Brooks is correct if it was a Homeowners policy now being transfer to an LLC and used as a rental. 

Sometimes, just knowing the rigth people...whether that’s sharp-minded agents who see a gem before it’s polished or a reliable contractor who’s not going to vanish mid-renovation...can make all the difference.If I had to do it all over again with $80K in my pocket, I’d jump on that first multifamily, rent it out, and let the tenants’ checks pay off the mortgage month after month.

If you fix it and have the receipt with a transferable warranty you should be OK.

but there is case law that allows you to break some terms of a mortgage agreement if something is unenforceable, for example the sub-to community relies on the Supreme Court cases which say it's not required to notify the lender when you transfer the deed/title. 

And as others said, section 8 tenants are often the most quiet and reliable because they don't want to lose this aid and they are grateful to have housing. 

However, in no event may a postponement period extend beyond: (a) the due date (including extensions) of the taxpayer’s tax return for the year of the transfer (See § 1.1031(k)-1(b)(2)(ii)); or (b) one year (See section 7508A(a)).(2) A taxpayer who is a transferor qualifies for a postponement under thissection only if--(a) The relinquished property was transferred on or before the dateof the federally declared disaster, or in a transaction governed by Rev.