However, the defender looks highly unlikely to be able to line up for the Pilgrims' National League North play-off semi-final.
Duxbury was taken to hospital midway through the first half after a collision of heads with Kidderminster Harriers keeper Luke Simpson in Thursday night's 2-1 victory, receiving 30-plus stitches to his lip.
The Boston left back wrote on social media that he believed he wouldn't be ready for Sunday's National League North play-off semi-final at AFC Fylde.
"Won't be a game for me Sunday but I'll be cheering the boys on," he said.
But manager Cox wasn't so sure, holding out some hope.
"It was a really bad gash on his lip," he said.
"Dux is a warrior and I'd like to think he'd be there or thereabouts."
It seems unlikely Duxbury will be cleared to play with the potential for the stitches to be opened op during the contest.
United went into Thursday's contest with seven players out injured, and Duxbury could still be number eight, joining Tom Platt, Jordan Burrow, Jay Rollins, Matt Tootle, Joe Leesley, Brad Nicholson and Connor Shanks on the list.
"We're losing players at the minute, we've got more out on crutches than playing on the pitch," Cox added.
"But his (Duxbury's) health is more important than anything. Fergie (Keenan Ferguson) has come on and not put a foot wrong."
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