Sellers may be reluctant to accept an offer that is contingent on the sale of another property, but a sale can be structured to minimize the risks.
The seller should put a limit on the amount of time that the buyers have to accept an offer, and they should keep their home on the market. They should also reserve the right to require that any contingencies be met within a short period of time (24-48 hours) if they get a second offer. This is called a "First Right" contingency.
Contingent sales can work well for the sellers. The buyer is not in a position to ask for concessions on price or terms and may be able to get interim financing. Each situation is different, however, so go over the terms with your agent before accepting a contingent offer.