This kitty definitely needs medical attention ASAP. Yes, your co-worker should trap him. Usually humane societies or shelters have traps to lend - they will require a deposit which will be returned when the trap is.
The floor of the trap should be lined with cardboard cut to fit - if newspaper is used and it blows around, it will scare the cat away. Don't put cardboard on the trip mechanism itself. The cardboard will make it more comfortable for the cat to sit on once he's trapped.
If the trap can be put into bushes or under evergreen tree boughs to camouflage it, that will help. You can drape a large dark-colored towel over the trap as well - it helps to disguise the trap. You'll want to cover the trap in any case as soon as the cat is in it. It will calm him and make him feel safer.
Under no circumstances should the trap be left unattended. Your coworker should stay and watch from a distance while she's attempting to trap.
Many people have success with very smelly foods - tuna or sardines, for example. Some swear by KFC!!! Put just a bite of food at the entrance to the trap, another bite near the trip plate, and a small amount at the back of the trap. The hungrier kitty is the more motivated he'll be to go in. Ideally, if you can withhold food for 24 hours and then trap, your odds of getting kitty will improve. Your co-worker also needs to find a vet who is willing to handle a feral kitty. She should do this ASAP. Tell her to get a reference from the local shelter or humane society. Vets who work with ferals know that it's usually impossible to stick to a set appointment, so they will give you a tentative one. If you don't get the kitty, call the vet right away to let them know and re-schedule. The kitty can be kept in the trap if necessary overnite, but try not to make it any longer than that. Keep the trap covered, but lift the towel up at one end for ventilation and don't put it anywhere that's too warm. Face that end away from any view of people. Keep the trap in as quiet a spot as possible. Don't try to transfer the kitty to a carrier. Take him to the vet in the covered trap.
Regarding the fox - I'd hate to see him put down which is what may happen if Animal Control is called. On the other hand , he could very likely be the culprit in this poor kitty's injury and if so, it's obviously dangerous for the cat to continue to be exposed to him. Your coworker could call Animal Control and ask what their protocol is in this situation. Hopefully they can remove and relocate him. Tell her not to mention anything about the feral cat - she doesn't want Animal Control trying to trap ferals in your area since they WILL put the cats down.
Please tell you coworker she's wonderful to be taking care of this poor little guy. If he hasn't already been neutered, when she traps him, she should get that taken care of too. I wish her and this kitty lots of good luck.