CHICAGO (CBS) -- A man made back to his Woodlawn neighborhood home with police on his tail, but died of injuries he suffered when a glass door shattered as he ran right through it.

Jonrynn Avery, 24, of the 6200 block of South Vernon Avenue, was pronounced dead at 9:09 p.m. Monday at Stroger Hospital of Cook County, police said.

At 8:25 p.m., police saw the man firing a handgun, and began chasing him, a source said.

He ran clear through a glass door at his house, and suffered multiple cuts, police said.

Wentworth Area detectives are investigating the incident as a non-criminal death, police said.

The Sun-Times Media Wire contributed to this report.