“Our goal is to be just and timely in compensating all of the families who lost loved ones and those who suffered serious physical injury,” the company said in a statement.

G.M. declined to say whether it had made a specific effort to reach the Averills and the 12 other families identified by G.M.

Until now, Ms. Averill’s family said they believed she had probably died of a stroke while driving. Ms. Averill was 81, the matriarch of a family that has grown fruits and vegetables on a farm in Connecticut since 1746. A widow, she was fit and active, swimming often and helping at the family’s farm stand during the busiest months.

Now, family members find themselves in a race against the calendar if they are to receive compensation from the victims’ fund administered by the compensation specialist Kenneth Feinberg. The fund has committed to making payments to the families of 32 people who died and 35 others who were injured because of the faulty switch.

Ms. Averill’s relatives say they are considering filing a claim — payments in the case of a death are almost certainly more than the $1 million starting point — but with a deadline of Dec. 31, they have come to the process late.

The family said it would consider suing, but it cannot because G.M. has protection from litigation involving incidents that occurred before the company emerged from bankruptcy in 2009. That protection is being challenged in court, though G.M. has waived its shield in the cases Mr. Feinberg approves.