An ordinary case of the flu can kill people already weakened by chronic illness, so federal health officials are now recommending that people living with such high-risk patients get flu shots.

The national Centers for Disease Control had previously recommended influenza vaccinations for those at high risk of flu-related complications, including nursing home residents with chronic illnesses and people with chronic heart, lung or circulatory disease and for those who give medical care to high-risk people.

In its recommendations released last week, the CDC's Immunization Practices Advisory Committee added to that list anyone in the same household as a high-risk patient.

"It makes sense, knowing how home care works," said Nancy Arden, a CDC flu specialist. "A lot of times, family members provide a lot of care in the home. It was felt that since influenza is quite contagious, really, to provide optimal protection {of the high-risk patient} it would probably be best to require vaccination of all household contacts."

The immunization committee's statement also included final approval of the formula for the flu vaccine for the nation's 1987-88 winter flu season, a three-way flu shot incorporating the ingredient in last winter's special supplemental Taiwan flu vaccine.

In addition to the vaccine for the Taiwan strain, the recommended 1987-88 vaccine will also contain protection against the Leningrad flu and the Ann Arbor flu. The vaccine will be available starting this fall.