With his index finger he spelled, one capital letter at a time, the words “I LOVE YOU.”

“Oh, you love me?” she told him. “That’s so sweet. Thank you.”

It was the first time she had responded in any significant way to the many attempts to communicate with her. In her disoriented state, she thought he was a kind stranger. “It wasn’t even a conversation,” Mr. Lundgard said. “It was just that one exchange which alerted me to the fact that she was not damaged to such an extent that it was beyond her ability to recover.”

Mr. Lundgard later had a longer conversation with Ms. Gossiaux, in which he finger-spelled questions and she responded. It took a long time to spell one sentence, but she understood what he wrote on her palm, telling him what year it was and where she was born.

Shortly after, she allowed her hearing aid to be put in her right ear. In an instant, she was back. “When she came to, it was like a party in the hospital,” said Mr. Lundgard, who is taking a year off from Cooper to help his girlfriend; he is a seasonal employee at The New York Times, working as an art assistant. “All the nurses came in; they were, like, dancing and screaming.”

Ms. Gossiaux never went to a nursing home. She was transferred to NYU Langone Medical Center’s Rusk Institute of Rehabilitation Medicine on East 17th Street, where she has been undergoing physical therapy.

Fate seems a meager word to describe the great mystery of their lives. On the morning of the accident, Mr. Lundgard put her helmet on her, strapping it on tight. A bus driver at the Louisiana school district where Susan Gossiaux works  a woman Ms. Gossiaux’s mother had never met  donated 106.5 sick days so that she could be by her daughter’s side. After the nurse told her that her daughter was gone, Susan Gossiaux was whispering in her ear when Ms. Gossiaux suddenly raised her arm.