It is possible to catch foxes. Although, the odd time they will excape . My farm is called "yay for hay" i had 4 foxes for a few days now and it wasnt untill this morning when one excaped theough the fencing. I traped them with the white fencing and added a raspberry bush. If you do not have a raspberry bush in their pen, they will disapear so make sure you have a berry bush. Also, like the frogs, they MUST have a large enough pen other wise they will just walk through the fencing. - found all this from experience. Good luck!
Also, for getting rid of them,
A) they like berrie bushes and will come if u have one
B) they do not like dogs (apparently)
C) they come when there is treasure on your property... ( apparently)