Yes, I've done this.
You don't have to end the auction, otherwise you have to go through allt he listing process again. What I do is to "Revise your item" by adding the BIN price to the listing (you have to pay a small fee for BIN, but hey ho), and then list it with an auction price AND a BIN price.
However, before you do that I'd contact the person who's offered you that price, telling them that you're about to do this so they can bid straight away as soon as the BIN price is added - otherwise someone else might nip in before them and pip them to the post!
As soon as you list it, and the buyer buys it on the BIN basis, the auction ends and the item listing finishes. I hope this helps.