14 April 2017 Last updated at 01:06 BST
They threw him a one-week birthday party, then a two-week party and then a one-month party.
This year he'll be celebrating his 12th birthday.
"Even if I had just a little time, I wanted that with him," says his mum, Ellen.
Hayden's parents were told their son wouldn't feel, eat, think, breathe or hear after he had a brain bleed and a stroke.
He and Samuel were interviewed by Chris Ulmer, a former special education teacher who travels the world helping people with disabilities tell their stories.
Now five, Hayden "brings joy to everyone he encounters", says Chris.
Chris posts the videos on his Facebook page Special Books by Special Kids (SBSK), which has more than one million followers.
Ellen blogs about Samuel's journey here.
This is the third video in a series about Chris's work. Watch the other ones on our Facebook page.
Video Journalist: Hannah Gelbart
When Samuel was born with a rare form of dwarfism, his parents were told he only had a few months to live.