In the fashion industry, perhaps more than in any other business, the survival of a company often rests heavily on the shoulders of a single individual. Yet for most prominent fashion designers, their ambition is to create something so distinctive, so much the trademark of a single mind, that it is almost blasphemy to talk about designating a successor.

That is just one of many ways that Gianni Versace, who created one of the world’s great fashion empires, was different from his peers. A brush with cancer in 1993 made Mr. Versace keenly aware of his own mortality. He took steps to see that his collections would continue, that his family would be taken care of and that there was a figure to look to for leadership and creativity after he was gone.

After escaping cancer’s grip, Mr. Versace died last Tuesday when he was shot in front of his home in Miami Beach. Although the fashion world was distraught, the carefully constructed template for the future of the business appears set to go forward, with Mr. Versace’s sister, Donatella, 40, taking the helm of the design side, and his brother Santo, 52, overseeing the finances. Indeed, the company may well be strong enough that after a period to regroup it will be in position to begin its long-anticipated initial public offering as early as next year.

If Gianni Versace Group survives its founder’s death, it will be joining a select group. And like the fashion houses that still thrive — Chanel, Christian Dior and Gucci among them — Versace appears to have several important traits. What separates the survivors from the also-rans are, among other things, a strong, internationally known name with diverse lines of products, a powerful new designer who can continue to infuse modernity into the company’s image and — perhaps most important — a signature item like the Chanel ”C” that a successor can easily pick up and run with.

Versace’s strength is that before he died the designer developed certain characteristic flourishes, including the Medusa head logo and a flamboyant, sexy fashion image.

”A house’s life depends upon those kinds of signature elements,” said Richard Martin, the curator of the fashion and costume exhibition at the Metropolitan Museum of Art in New York. ”It can be as simple as the Medusa symbol or the idea of draping men’s shirts that cling to the body — things that can be perpetuated.”

Still, the fashion industry is replete with the graves of designers who took their houses down with them, from Norman Norell, who dressed lunching ladies in the 1950’s, to Perry Ellis, who died in 1986. Two decades after Anne Klein’s death, the company she founded shut down its designer collection division last year, after years of losses and the inability to recapture her magic touch.

Of course, the death of a fashion house has a much broader impact than society’s loss of slim skirts or boucle suits. The companies, which often generate hundreds of millions of dollars in annual revenues, fill retail stores with products, magazines with advertisements and employ everyone from sales representatives to thread and dye makers to models.

And while there have clearly been businesses in other fields that died with their leader, few seem to have such volatile succession issues. Indeed, companies like Wal-Mart and Walt Disney, for all their difficulty in coping with the loss of mythic-figure founders, have managed to prosper under new leadership.

”Succession in creative fields is more difficult because of your dependence on the energy and dynamism of the person doing the creating,” said Joyce Shields, a managing director at Hay McBer Management Consultants. ”Versace now will build on the strength of the sister, but there will probably be a different dynamic.”

The most significant example of creative singularity may have been the vaunted House of Chanel.

After the death of Coco Chanel in 1971, the strong signature items were there, but the house desperately needed a designer to modernize the tradition. Although new designers were brought in, the clothing that once defined chic became associated with dusty old society ladies, the house more a museum than production house. Chanel floundered until the designer Karl Lagerfeld joined it in 1983.

”The house continued, but was completely boring,” said Valerie Steele, the chief curator of the museum at the Fashion Institute of Technology. ”It picked up when Lagerfeld came in with a mandate to update.”

Revisiting the Chanel annals, Mr. Lagerfeld brought back Coco’s Chanel’s famous navy suit, but it was given white pique collars and revers. Her pumps made their way down the runway, initials and all. Mr. Lagerfeld, retaining the signature gardenia, also plastered white pique flowers on suit shoulders. In more recent collections, he has take the Chanel ”C” and attached it to a very modern string bikini.

Gucci is an example of a house that fell on hard times but then rose again to be even bigger and better than in its halcyon era. The company’s signature horse bit, which adorned pocketbooks, belts and scarves of cafe society and the Hollywood set in the 1950’s and 1960’s, was such a powerful symbol that it allowed the company to reinvent itself after it had fallen into disarray in the 1970’s and 1980’s because of family bickering and fiscal mismanagement.

When Dawn Mello became creative director in 1989, she set her sights on getting fresh, hot design talent to come in, dust off the image and start anew. It helped that she had the backing of the Investcorp, a finance group known for taking tired brand names, infusing them with strong management and putting them back on the streets.

The transition took a while and was not without turmoil. While Gucci had never before had a true ready-to-wear line, Tom Ford, the current darling of Seventh Avenue, was brought in to create one. He cleverly twisted Gucci’s retro image into modern fashion: velvet hip-huggers and shiny shirts. The company has since watched its earnings soar and its newly public stock go through the roof.

The success of Gucci underscores another important survival necessity among fashion houses: diversity. While few women can afford a $400 buttonless Gucci shirt, many can buy a pair of shoes, a handbag, a bottle of perfume or a scarf. And Gucci has built a global image able to withstand the vagaries of individual markets.

Compare this with Norell. Although Norman Norell was the designer of women’s fashions in the 1950’s and 60’s, when he died in 1972, the house died with him.

”At the time of Norell’s popularity,” said Ms. Mello, who is now the president of Bergdorf Goodman, ”he appealed to a very limited group of affluent women who lived in major cities.” Unlike, say, Calvin Klein, no one had ever heard of Norman Norell jeans or underwear.

Being diversified, though, is not enough alone to keep a true collection afloat. When Perry Ellis died at age 46, retail experts were convinced that his many licensing agreements and widely known name would be enough for the house to live on.

But without a strong new designer to extend the original vision, a fashion house can lose its bearings. By the time Marc Jacobs was brought in to breathe fresh life into the collection in 1989, the Perry Ellis house had nothing to hold on to. Mr. Jacobs lost his job as house designer when he trotted out his grunge collection in 1993 — a set of flannel shirts that were a far cry from the slouchy suits of Ellis fame. Perry Ellis is now little more than a line of moderately priced men’s basics.

In many ways, Mr. Versace learned from those examples.

* By JENNIFER STEINHAUER, courtesy of New York Times, July 19, 1997.