Typically a property with an accepted offer will remain active in terms of showings and accepting offers until all of the contingencies in the contract are fulfilled.
This done as an attempt to minimize the damage, should the buyers not be able to fulfill the terms of the agreement.
Cash in and of itself does not necessarily make for a stronger offer, especially a self-proclaimed "lowball" offer. It's very hard to say which offer is more favorable since I'm not privy to all the details.
Thanks for commenting on my testimonials!
Best of Luck, SteveO