How is AR handled at closing?

Working Capital is part of the price (P). No ifs and buts. If seller keeps A/R, price (P) does not change, but the cash delivered reduces. It is unhealthy for both parties to let seller keep and collect the A/R. This is a complex subject. I have taught this subject for 15+ years. I wrote a book in 2007; but have not had time to publish it.
Even, the debt-free cash-free (DFCF) concept is an over-simplification. Example: If seller has accrued taxes, is that debt. No, it is not debt. Therefore, does it mean that buyer assumes that liability?

It could be handled in any fashion the parties agree to. And it might depend on special circumstances, the accounting used for revenue recognition (thus A/R), etc. But normally in the lower middle market a transaction purchase price on a total enterprise value basis assuming a cash-free, debt-free balance sheet means that working capital assets, of which A/R is one, and working capital liabilities are transferred to the buyer. This net working capital is part of the value of the business and treated just like other assets being acquired. In other words, included in the purchase price unless otherwise stated.

Hopefully you'll get a lot of useful input from those in the Searchfunder community who have great expertise in this area. Some here teach courses and lead seminars on this subject. But in any case $10 million is a pretty hefty number so it likely makes sense to involve an experienced advisor and transaction counsel before considering discussion of valuation and terms with the seller.