The former Texas Longhorn was touted to be picked within the seven rounds of the NFL Draft, but was passed on by all 32 teams in the selection process before being scooped up by Seattle as a free agent.
Jeffcoat told the Dallas Morning News: "That's what was enticing about Seattle. They see that chip you have and poke at it and keep poking at it to make it grow in a positive way.
"It becomes motivation to become better than you ever thought you could be."
Jeffcoat recorded 82 tackles and 13 sacks for the Longhorns in the 2013 season.