We have three fenced yards; one is a half acre of partially forested land, which backs up to additional native space and pond, lots of critters, rabbits, raccoons, possums, musk rats, etc. We run three to four basenjis in this yard. These are younger dogs, stronger lure courser. They have terrorized the critters to the point the critters do not enter the area, those that do end up in the critter cemetery. We do have coyotes which come down from the foothill during the winter, during this period we do not leave our dogs out at night.
Basenjis are very effective hunters, especially as a group. This is a trait I continue to emphases we should not lose in the breed. The most risk is with inexperienced dog, raccoons, possums can inflict serious injuries. Off to the vet again. More often our dogs inflict these injuries to each other by arguing who gets the critter carcass, rabbits or musk rats mainly.
Suggest you keep any solo inexperienced basenji in at night when these critters are most active to avoid the vet bill.
As for the invisible electric fence, I would only use one during periods which I was actually in the yard supervising the dog. I know with our dogs, the shock from the collar would not be enough to deter them from chasing a squirrel. Such a fence does not keep the coyotes or dogs at large out. Suggest you purchase a large kennel with chew proof roof and anti dig barrier about the base for period which you desire to leave him outside alone.