If their property does go under deposit, your sale will be based on how strong of a buyer they have for their home. So the transaction will become a long train of different buyers doing home inspections and getting mortgage commitments. All of this is very possible but just more risky of becoming a train wreck than a closing.
Marianne and Joe's description of what a Hubbard is below is spot on. I'll add that I discourage clients I represent from accepting offers which contain Hubbard clauses since, IMHO, they are really contingencies that are GREAT for Buyers who like your home and want to tie it up, but they are bad for you as a Seller since they essentially take your home off the market. I'm saying that because many agents will not be as enthusiastic about showing homes that are in "Pending-Show" or "Deposit - Show" status since they know a contract is in place already. That's not to say you can't have a successful transaction with that Buyer who's making the offer.
I've had that type of Buyer work fast with their Buyer's Broker and then get their home listed and under contract quickly (30-60 day) and then come back to me with a "clean" offer absent the Hubbard Clause. Your listing agent can keep in touch with that Buyer's agent if you get any new offers and they may come back to you without the Hubbard before their home is sold.
Best of luck with your sale.
Greg Hanner, Broker, REALTOR, e-PRO