In New Jersey, the home is typically changed in the MLS as in attorney review (AR) as soon as the contract is signed by both buyer and seller and has been delivered to the respective attorneys for their review.
Once attorney review is completed, it is listed as under contract (UC), and once it closes, then, and only then listed as sold (C or S).
However, legally during the ENTIRE period from signing to closing, another contract may be submitted to the sellers attorney, UNLESS THE SELLER PUTS IN WRITING that they are no longer accepting any offers, or are accepting back-up offers only !!
I have had a few of my listings remain active and showing for back-up offers (with a written note from the seller) all through the process until the buyers have met all their contingencies. (Nowadays it's not obtaining the mortgage commitment that can kill a transaction and this protects the seller a bit) but this is not typically what happens.
Hope that helps.