The following information is primarily referencing red foxes. The terms home range and territory are often used interchangeably, but they are different. Home range and territory sizes can vary greatly.
Home Range:
There are certain resources that are essential for the survival of any species, including foxes. The essential resources are usually dispersed across a wide area and may be spread out between several different habitats such as pastures, forests, farmland, and municipalities. Foxes adapt well to human activity and often live in close proximity. This area is usually found around a suitable den site in which a fox spends its time wandering and looking for food and water. This area is loosely termed the home range.
Territory:
In some cases the resources in this area are defended against intrusion and other foxes are driven out. These areas are referred to as territories. Therefore despite often being used interchangeably, a territory and a home range are not necessarily the same thing. A home range may overlap with other foxes, whereas a territory generally will not. However intruders of the opposite sex tend to be tolerated more than interlopers of the same sex in a territory. In some cases foxes may defend the whole area against intruders and therefore it is both home range and territory. If food is abundant, foxes may tolerate intruders in some or all areas. So, the presence or absence of food greatly influences territorial behavior. Therefore, the home range is the area traveled by any animal during its normal activity usually for the purpose of finding food, mating and rearing or caring for young. A species is considered territorial if each individual or family group defends an area from intrusion by other members of the same species.
Territory Size:
Territory size in foxes is determined by resource availability, especially the abundance of preferred prey. While the size of an fox's territory is largely determined by the distribution of resources across the area, the number of animals that can be supported (group size) is determined by the abundance and distribution of those resources. The number of animals a habitat can support is generally known as “carrying capacity”. As a result, territory size and group size may vary independently and there is no significant relationship between the size of a territory and the number of animals living in it. This is because a small territory with ample resources can support more animals than a larger one with fewer resources. During certain times of the year or certain years there may be more resources in the territory than the foxes require. This usually due to a proliferation of prey species in which the foxes are dependent on. Consequently there is probably less stress and as a result the offspring and other foxes may not be driven off and foxes may be less territorial. Therefore, the social and behavioral structures of foxes are very complex and may never be fully understood. There is tremendous variation in territorial behavior that is not fully understood. In some instances there is complete absence of territoriality in some areas, while in others the home range is aggressively defended. Because of this it is very difficult to come up with the size of an "average" fox territory. There are just too many complex interactions.
Therefore if a fox or foxes is/are removed (killed/trapped) in a certain area all the aforementioned information must be considered in re-occupancy of the created vacancy. But if sufficient resources (primarily food) are present, the area will be reoccupied if foxes are present. How long does this take? It is difficult if not impossible to answer that question. Also, other foxes may already be in the area. In addition there are other considerations that may have influence on the re-occupancy.