Female box turtles can lay eggs without the presence of a mate. There are two possibilities when this occurs:
1) If a mate has been present within 5 years, a female can lay fertile eggs, as they have the ability to store sperm after mating for at least this long (no cases beyond five years have been documented)
2) Without fertilization, a box turtle will still occasionally lay eggs. It is unclear what stimulates this, wether seasonal changes or variations encourage it, or what, but it can on rare occasions occur that a female will develop and lay unfertilized eggs. It is more likely to occur in animals living outdoors experiencing seasonal changes, and would happen similarly timed to animals with normal mating.
Keeping box turtles indoors is not a successful long term method without great pains (and expensive ones) being taken to mimic nature in seasons and weather in great detail. Their breeding capability also fades after several years without a hibernation cycle and to some extent without outdoor living. For best health, an outdoor pen is the easiest and healtheist way for a north american box turtle to live.