No. Just no. Relocating wildlife is a bad idea, usually illegal, and is less humane than torturing the poor thing to death. Wildlife and game offices do not trap and relocate wildlife for the public. If they do, it is a huge waste of tax money. Usually they enforce the laws prohibiting wildlife relocation, and in the few backwards states that still allow it, they certainly aren't going to provide that service free of charge, when their job is to manage game for hunters. There are people that provide this service in the private sector, but you have to pay them, and they have to follow state laws on relocation, and most of the knowledgeable ones know better than relocating an animal because of the countless studies on how ineffective, or in some cases, dangerous or cruel, it is. The foxes that live out in whatever place it is that you suggest relocating to do not want your diseased and sick fox competing for their food until they can drive it to another chicken farm or to starvation. In the event that you actually put forth the effort to drive far enough that it won't be home by the next morning, which will take the better part of a tank of gas, it is likely to die a miserable death and take other innocent animals with it through whatever disease it harbors that the new location is not used to. Let me take you to North Korea and kick you out of the plane and see how you do. This is what it is like for relocated animals. Foxes are highly social. They will kill strangers at certain times of the year, and at others they will simply just out-compete them for food sources, as they have generations of acquired conditioning built up regarding what food sources there are in that area. Please consider flogging them to death with a section of garden hose before relocating, it would be a more humane end, and come much sooner.
While I agree with you that it's not a good idea to relocate, often illegal,
You make it sound like every critter that is trapped are "diseased or sick". Definitely not true...