Yes, foxes will definitely take hedgehogs. Not all foxes, but definitely some. Some foxes become specialist hedgehog catchers. One method is to wait until the hog is eating and therefore unrolled, when the fox will pounce at the soft belly area. Sadly once they have learned the technique they are likely to try again. That is the reason why I am always a bit sad to see images of hogs and foxes eating side by side. Foxes are predators and cannot be trusted and a hog eating right next to a fox is very vulnerable.
But re. the feed box, one of my boxes entrance is about 4 x 5 inches, but I have a brick 2 inches high just inside the doorway. Even large hogs have no problem accessing the box. But even cats can push up the lid unless it is securely either screwed down or has something pretty heavy on top.
The hog may not have felt safe going into the box. It seems entirely possible that it still smelt of foxes, even after being cleaned. (Hogs’ sense of smell if much more sensitive than ours.) But anyway, if the fox was still around the hog may not have wanted to risk being trapped in the box. If that fox has become a specialist hog catcher, it could easily wait for the hog to come out and catch it that way. Foxes can be incredibly patient if they think they’re going to get a meal.
I think if it was me, I might be inclined to leave off feeding the hogs for a while and hope the fox moved on elsewhere. The hogs can get lulled into a false sense of security when eating food provided for them by humans – when I imagine they would remain more alert when foraging for natural food.
Having said all that, hogs will move nests – not least to prevent a build up of parasites. i.e. they don’t normally use a hog box as a permanent home. (There need to be a variety of daytime ‘nesting’ places available for the hogs). So the hog may have moved out before the fox got in the box. But hogs need several gardens – unless it is enormous, one garden is not enough. Hogs can travel as much as 2 miles a night. So the best thing to do is to encourage your neighbours to have hog holes in their fences – or at least dig accessways under the fences.
Good luck. I hope you manage to find some sort of resolution to the probllem.