Basenjis are hunters, and if a cat, rabbit or dog is outside the electric fence, they will usually "take the hit" and run right through it, and not come back. They are also without defense for any big dog/critter that comes into your yard. I think the people that use them successfully are always out with the basenji when it is in the yard. Not left in the yard alone with just an electric 'sting' to keep them safe
Basenjis love to be outside to lie in the sun, but not all the time. They need to be family members, in the house with your family, cuddling and sitting with you on the couch, probably sleeping in your bed. They are pack animals and you become their pack. They need lots of stimulation and interaction to be happy. They are not "yard dogs", they are thinking, feeling beings who love to interact with their pack.
If this is not the way you want a dog to be, a basenji may not be the best dog for you.