Before the paths of Jason Volz and Carlton McPherson collided in a terrible moment on a Harlem subway platform on Monday, their lives had seemed to be heading in opposite directions.

Mr. McPherson had been hospitalized at least half a dozen times since last year for mental health treatment, according to someone who has seen some of his medical records. A neighbor in the Bronx said he sometimes slept in a hallway closet in his grandmother’s building because she would not let him into her apartment. Last October, a man whom prosecutors believe to be Mr. McPherson — he had the same name and birth year — was charged with beating a Brooklyn homeless shelter employee with a cane.

Mr. Volz, 54, was recovering from addiction and had also endured homelessness, but had gotten sober two years ago and had just moved into a new apartment, his ex-wife said.

On Monday night, the police say, Mr. McPherson, 24, walked up to Mr. Volz on the uptown platform of the 125th Street station on Lexington Avenue and shoved him in front of an oncoming No. 4 train.

Responding police officers, who had been on another part of the platform, found him lifeless beneath the train. His death was a recurrence of the ultimate New York City nightmare, and another example of the difficulty of preventing violence on the subway despite years of efforts by state and city authorities to keep people struggling with severe mental illness out of the transit system.

Mayor Eric Adams, who has watched crime in the subway largely defy his attempts to rein it in, sounded a note of defeat on Tuesday, acknowledging that the presence of police officers had not been enough to stop Monday’s attack.