From Wiktionary, the free dictionary
From non- + qualifier.
nonqualifier (plural nonqualifiers)
- One who fails to qualify.
2008 May 18, Viv Bernstein, “Kahne Proves Fans’ Faith Was Well Placed”, in New York Times[1]:And he came up short in the Sprint Showdown race for nonqualifiers earlier in the night, failing to finish high enough to advance to the main event.