POLITE APPLAUSE LEAVING LAS VEGAS: Drama. Starring Nicolas Cage and Elisabeth Shue. Directed by Mike Figgis. (R. 115 minutes.)

'Leaving Las Vegas" is a haunting little story about a couple of damaged people who meet, fall in love and remain damaged -- but at least they have company. It's an enjoyable, sometimes fascinating film, and it grows in the memory.

Written and directed by Mike Figgis ("Internal Affairs") and now on home video, the film is based on the John O'Brien novel of the same name.

The picture stars Nicolas Cage, who plays Ben, a failed, drunken writer, the kind of drunk for whom the word "alcoholic" is just too pale. He is a falling-down, gasping-for-breath, losing-his-job, shaking-with-spasms drunk, a man well on his way to drinking himself into the grave.

Cage is extraordinary in the pre-credits sequence, in which he's shown bopping around a supermarket, filling a shopping cart with liquor bottles. He borrows money, goes on a bender and tries to pick up a woman: "You smell great, you look great." When his boss lets him go, he bursts into tears. He's like an infant, helpless and exploding with need.

When he goes to Las Vegas with the idea of drinking himself to death, he meets Sera, a high- priced hooker, played by Elisabeth Shue. Until now, Shue has had little chance in movies to play any thing but a pleasing ingenue, but in "Leaving Las Vegas" she shows herself to be a contender.

Figgis manages to make Ben and Sera's attraction understandable, yet he also gives it a mystical edge. They're both intelligent, benign and wounded. They also seem to be made for each other on a level that can't be explained.

Unlike most love stories, "Leaving Las Vegas" is not about redemption, just love, so it can't go in the usual directions. The film never compromises. There are no interludes of uninterrupted good times. Ben is a raving mess, and sooner or later all good days turn sour. Ben's physical deterioration is conveyed by Cage in detail. Watching him, it's hard to remember this is a healthy actor only pretending to be sick.

Cage's great performance is matched by Shue, who becomes the focus by the middle of the picture. She plays Sera with tenderness and a lack of sentiment.