If there are feral cats in the area then the area is already imbalanced and no longer a pristine native area. So all the rules of what balances what are pointless. What matters is what balance is being produced by the interchange of existing and transitory predators as they move through the area looking for prey that they can catch.
From the tone of your comments, you are regarding the Red Fox as alien. However the species and its subspecies has been on this continent for over 100,000 years. So then it is a part of a pristine native habitat.
You need to define whether or not the habitat you are looking at is indeed pristine native or suburban in nature. While a suburban area is seen as native habitat the onsite presence of men and human activity, such as farming, by its nature strips away any semblance of purity and represents an intrusion and adulteration of the natural world. Rules regarding predator and fair game go out the door.
If you consider the beast to be too dominant and destructive of other animal populations then my best advice is to provide it a feeding station where appropriate food, such as canned dog food, can be provided on an intermittent basis only to supplement its diet and provide some relief from over-predation.

Primary wooded area. I live in rural section of town. Terrestrial_man, the fox has always been there. However, in the Mid 70's they decided to kill all the coyotes that were living in the area because they were killing livestock. This has led along with buildings and developments. Now the Fox doesn't have a natural predator. We have not spotted a groundhog, raccoon, possum, & a rabbits in about a year. But we hear that fox every 3 to 4 nights looking for prey. We had a very cold winter in 2014, and that could contribute to the reduction. I just believe the fox is the reason. We got plenty of deer.

Foxes are on the top of the food chain. They are not prey animas, so they generally do not have predators.

They generally eat small prey like mice and squirrels. Not the larger mammals you listed.

Predators do not extinguish the prey population. Think about it: how could they survive if there were no prey left?

Don't worry. Keep cats indoors. If there are feral strays, get them to a shelter so they are not prey for real, native predators.

We
have Red fox that appears to not have any predators by headwaywriters.com. We have not seen a groundhog,
rabbits, and we by and by know it has eaten