Police hoped the author of the note would come forward with more information about the situation.
Police have identified the teen as 18-year-old James Clinton and said he remained unconscious and in critical condition.
The investigation began Monday night with the note to police at the University of Alaska Anchorage. Chief Rick Shell said two officers were on duty at their desks in a squad room about 8:30 p.m. when one of them spotted it on the floor.
"He picked it up, read it, let the other officer read it," Shell said. "The other officer saw content that led him to believe that the Anchorage Police Department should be involved."
Officers drove to the nearby home in downtown Anchorage and found Clinton being held against his will in the basement. Asked if anyone was at the home with Clinton when officers arrived, Anchorage police spokeswoman Anita Shell said detectives were not releasing that information.
The man's injuries were extensive, she said.
"It's my understanding he was beaten around the head and the face, the whole body," she said.
The home was owned by Covenant House, which operates a shelter for homeless teenagers across the street. Director Alison Kear said the home was scheduled to be knocked down Wednesday to expand a parking lot.
Wrought iron mesh had covered the windows and doors were locked, Kear said. A security company had patrolled outside. The only access she could guess was a second-floor window not much bigger than a dog door.
"How they were able to enter there is perplexing to me," she said.
Shell could not say Thursday whether the crime scene was the abandoned home or elsewhere."We have not yet spoken to the young man because of his medical state," she said.
In either case, she said, investigators allowed a scheduled demolition of the home to move forward and a wrecking crew used heavy machinery on Thursday to knock down the building.
University Police Chief Shell praised the quick response by both departments.
"This was just an absolutely outstanding case of two officers taking something that could have been fairly innocuous and taking it seriously," Shell said. "It ended up saving the young man's life."