Constance (Diane Lane) and Edward (Richard Gere) both realize that the other has figured out their secret (he knows she was cheating, and she knows he killed her lover), and they do their best to cover up for each other. They si tin the car and talk about selling everything and escaping to Mexico or Tahiti or someplace before the police can put together the pieces. As the camera pulls away for the closing shot, we realize that they are stopped in front of a police station. The viewer is left wondering whether they actually make their escape or if Edward turns himself in.
Thanks, LisaEsca, and others who clarified the ending!
Laura H adds that on the DVD extras, "Edward actually goes INTO the police station and turns himself in. His wife and son go back home to live their life!"

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