AFAIK players are allowed to move to non-league clubs on loan, but anywhere in the league is only allowed during the transfer windows.
It's a big problem for injured players, they struggle to get the game time to properly regain fitness at their parent club, but can't drop down a league unless they're willing to be there for 4 months or so.
I think it's part of the reason why we ended up getting Dougall, he was well liked at Barnsley, at least by the fans, but he had a bad injury towards the tail end of the 2018/19 season then struggled to get back into the team, possibly with some other injury problems as well.