I actually have experience with this. I placed a dog with someone who - in spite of what I said about they can NEVER be off leash, they thought that way out in the country with an electronic collar would be fine.
They didn't notice that the batteries were weak, gravel truck down road, basenji dead.
Basenjis are not an off leash dog - they are hunters and if they see it or smell it they are gone. NO you cannot train that out of them. They have been hunters for thousands of years and will ALWAYS revert to that.
re: allergies. Here is something that I do when people say they have allergies.
Use a cotton swab (q-tip) to swab inside the dogs mouth and set on a paper towel.
Take a very fine tooth come and scrape on the skin of the dog in several different places and wipe off the skin dander and hair (even if you get a little) on the paper towel as well.
Fold it up and put it under the pillow of the person with the allergies. If they break out or have a runny nose - the dog most likely won't work for you.