Woods, 31, has signed for Bradford City until the end of the season, bringing to an end a four-and-a-half year stay at Deepdale.
Injury limited his game-time in the last three seasons, with him missing all of the 2016/17 campaign with a torn cruciate ligament.
He made 18 appearances last season, while a hamstring injury suffered in August has seen him play just twice.
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Woods has been fit and back in the squad since the start of December but others were ahead of him.
Neil said: “I just felt that we couldn’t get him going because every time we got him fit, Calum broke down.
“I had a good chat with him the other night and thanked him for what he had done for the club.
“Calum was an absolute model professional, even when he wasn’t playing.
“He was great about the place, a really great lad and a really good player.
“I think Bradford have got a really good player on their hands.
“We like to look after our players.
“I have a duty to the club but I have a duty to the players too.
“Calum is such a good lad and has been a great professional for us.
“That is why we wanted to assist him we much as we could.
“If he goes to Bradford and does exactly what I think he can do, he should not be short of offers come the summer.”
Woods joined North End on a Bosman in June 2014 after leaving Huddersfield.
He was in the team which won the League One play-off final at Wembley in May 2015.
In PNE’s first season in the Championship, Woods made 35 appearances and that was arguably his best spell.
He suffered the serious knee injury in a pre-season game at Oldham in July 2016, which saw him ruled out for the full campaign.