THIS MUCH is undisputed about Kathleen Tiernan: she was 5-foot-7, blue-eyed and freckled, and embarrassed about her weight. She had a broad and intelligent sense of humor. She lived alone in a studio apartment, she dated one man regularly, and she worked as a guidance counselor and algebra teacher at Notre Dame High School in Belmont, Calif.

In the late summer of 1982, sometime before her heart stopped, she lost about 25 pounds--all of it, her family's lawyers allege, on the Cambridge Diet. Kathleen Tiernan died Oct. 11, 1982, after 18 days in a coma. She had slumped to the floor in the entranceway of a restaurant where she was to join her boyfriend for dinner (Tiernan had begun eating food again); by the time paramedics used electric shock to start her heart again, Tiernan had been in cardiac arrest for about seven minutes.

Last December, after several consultations with a San Francisco lawyer and physicians who reviewed Tiernan's records, her sister and mother sued Cambridge Plan International for designing and marketing a product the complaint calls "defective and unwholesome and deleterious to human health." Cambridge attorney John Banker says he cannot yet discuss the specifics of the Tiernan case, except to say that he firmly believes the diet is safe. "I think we're going to wind up proving that the diet was not the cause of her death," he says.

The suit will not be heard for at least six months, but it has become one of the focal points for the longstanding controversy about whether it is safe to have nationwide independent sales people distributing a diet that provides only 330 calories a day.

"This was something that should not have happened," says Tiernan's older sister Terese Tiernan-Tanis, an archivist who lives in Los Angeles. "She didn't smoke, she rarely drank, she didn't touch dope--of all of us, she was the cleanest liver."

It was Tiernan's medical history, both before and after her heart failure, that convinced San Francisco attorney Stephen Cox to accept the case. According to San Francisco cardiologist William Breall, who reviewed the young woman's records at Cox's request, Tiernan showed no evidence of prior coronary disease, and her electrocardiograms revealed an irregularity in "QT wave," which is one of the measurements of electrical activity in the heart.

That particular irregularity, Breall says, was one of the classic findings in the cases of some dieters, many of them young and without prior history of heart disease, who died while losing weight with "liquid protein," a diet product popular during the late 1970s. Doctors are not certain just what in the liquid protein might provoke the odd wave pattern--loss of potassium or other minerals is one theory that has been examined. The diet is quite different from liquid protein, according to Robert O. Nesheim, Cambridge International's vice president for science and technology. Nesheim says Cambridge uses much better quality protein and has been enormously well researched to provide the dieter with 100 percent of the recommended daily allowance of every known nutrient.

Many physicians agree with the official statement adopted two years ago by the American Society of Bariatric Physicians, or obesity specialists: all very low-calorie diets "pose a significant health hazard to dieters not under continuous and immediate medical supervision by a physician knowledgeable in the metabolism and nutrition of such diets."

"Anything that represents a change from the traditional methods of using food and losing weight by pushing yourself away from the table tends to be resisted," says Nesheim. "If this condition that people have been alluding to was really a serious concern, we would have had a significant number of incidents that would have shown up."

Nesheim, who came to Cambridge after a long career at Quaker Oats, says 5 million people have used the diet since the Feathers first brought it to the United States. With numbers that high, he says, the reported rate of cardiac arrest deaths is, in fact, well below the percentage of deaths that occur in the population as a whole. "If, in fact, the diet did cause the death of one person, obviously any death is too many," Nesheim says. "On the other hand, people who are severely obese have some risks, and there is a trade-off in that regard."

The United States Food and Drug Administration warned in late 1977 that liquid protein diets could be fatal, which helped ruin sales of the diet drink. The FDA has issued no specific warnings against the Cambridge Diet. The agency has issued several broadly worded warnings about the dangers of undertaking low-calorie diets without medical supervision, but FDA has found no reason to recall or halt distribution of the Cambridge Diet, the spokesman said.