Unless you drive 25 miles, you are not taking it far enough away that it won't be back. If you do take it far enough that it won't come back, you are releasing an animal unfamiliar with it's surroundings into territory occupied with members of it's species and predators that do. If it manages to survive, it will likely be pushed back into similar food niches, ie humans. Except now it will be reluctant to enter a trap. If it survives. Very likely that it will get chewed up by members of it's own species as they defend their territory, or starve as it is pushed from one territory to another. If it is a fox, it is likely that if the average backyard chicken keeper got it to go in a trap in the first place, there was something wrong with it. There are diseases that have a very long dormancy period, others are held in check by a healthy immune system but an animal in a weakened state can become a disease vector. Exposure risk is very high, as members of it's own species will have close contact as they attack it to drive it out of their territory or kill it. As it gets driven from territory to territory it might pick up diseases from it's attackers, supposing it is healthy enough to survive the first encounter. Lacking a family unit for defense, it will be driven from territory to territory, possibly spreading disease and parasites. This potential disease transmission could be held in check by natural or regularly occurring population barriers, such as a mountain, a river, the edge of an urban area, an interstate highway, etc. When you translocate, you might take strains of parasites from one population and introduce it to a population that has no immunity or resistance to that strain of disease or parasite. Relocating is either completely ineffective, or potentially fatal to the animal you are relocating, and possibly vast numbers of the same species, depending on how far you go. Any death resulting from relocation is likely to be much less humane than anything inflicted directly by human means, possibly taking months of suffering to reach fatality. Things like starvation, or not being able to find a den during a cold snap and getting frostbite which leads to gangrene are not pretty ways to go.