Film producer James Ballard (James Spader) and his wife, Catherine (Deborah Kara Unger), are in an open marriage. The couple engage in various infidelities but, between them, have unenthusiastic sex. Their arousal is heightened by discussing the intimate details of their extramarital sex.
While driving home from work late one night, Ballard's car collides head-on with another, killing its male passenger. While trapped in the fused wreckage, the driver, Dr. Helen Remington (Holly Hunter), wife of the dead passenger, exposes a breast to Ballard when she pulls off the shoulder harness of her seat belt.
While recovering, Ballard meets Remington again, as well as a man named Vaughan (Elias Koteas), who takes a keen interest in the brace holding Ballard's shattered leg together and photographs it. While leaving the hospital, Remington and Ballard begin an affair, one primarily fueled by their shared experience of the car crash (not only do all of their sexual assignations take place in cars, all of Remington's off-screen sexual encounters take place in cars as well). In an attempt to make some sense of why they are so aroused by their car wreck, they go to see one of Vaughan's cult meetings/performance pieces, a re-creation of the car crash that killed James Dean with authentic cars and stunt drivers. When Transport Ministry officials break up the event, Ballard flees with Remington and Vaughan.
Ballard becomes one of Vaughan's followers who fetishize car crashes, obsessively watching car safety test videos and photographing traffic collisions. Ballard drives Vaughan's Lincoln convertible around the city while Vaughan picks up and uses street prostitutes and, later, Ballard's wife. In turn, Ballard has a dalliance with one of the other group members, Gabrielle (Rosanna Arquette), a beautiful woman whose legs are clad in restrictive steel braces and who has a vulva-like scar on the back of one of her thighs, which is used as a substitute for a vagina by Ballard. The film's sexual couplings in (or involving) cars are not restricted to heterosexual experiences. While watching videos of car crashes, Remington becomes extremely aroused and gropes the crotches of both Ballard and Gabrielle, suggesting an imminent mĂŠnage Ă  trois. Instead, Vaughan and Ballard eventually turn towards each other and have sex while, later, Gabrielle and Remington have sex with each other.
Though Vaughan claims at first that he is interested in the "reshaping of the human body by modern technology," in fact his project is to live out the philosophy that the car crash is a "fertilizing rather than a destructive event, mediating the sexuality of those who have died with an intensity that's impossible in any other form."
The film's climax begins with Vaughan's death and ends with Ballard being involved in another semi-deliberate car crash, this one involving his wife. Their fetish for car crashes has, ironically enough, had an unusual bonding effect on the Ballards' marriage. As he caresses her bruised body on the grass median near the crash, Ballard and his wife display affection for each other, ending with Ballard saying, "Maybe the next one," possibly implying that the logical end result of their extreme fetish is death.

Question: When did Ballard meet Vaughan?
Answer: While recovering from a car accident.
Alternative answer: In the hospital