All good suggestions so far for you to try. Here's my suggestions based on my experiences.
1. When mine first came to my home I would arrange a bit of vacation time so that the first day I was with them totally, then the next day I would disappear out the door for 15 minutes and then for longer times, then the third day I disappeared for an hour or more, etc., until I could go to work for half a day then eventually for my full regular work day. This took me about a week to train the dog to be home alone.
2. The second basenji that came into my life had been broken of his crate training by an ignorant owner so I never could get him back into it. Instead I blocked off a corner of the kitchen for him with a bed and toys for him to stay in for the first several days. Gradually I allowed him more wandering room until he was trustworthy enough to have access to the whole house. This took about a month.
3. Be sure to give your dog a variety of toys and especially the kind that you can put kibble or other food in (such as "Kong" toys). Basenjis need mental stimulation or they get bored (=destructive). My current basenji gets frozen raw marrow bones when I go to work and sometimes she'll still be nawing on it when I get home. I also save old bones and fill the hole with kibble and yogurt or pumpkin and then freeze and give this to her sometimes.
4. Someone mentioned rawhide but I've never had luck with that - it's not digestable and has caused problems with my dogs (one time a piece got stuck in the digestive tract and he screamed "bloody murder" with every movement). Never give your dog a treat unsupervised until you know she can handle it or doesn't have an allergic reaction to it. Once you know its safe then okay - but even then I never give the stick type treats to mine unless I'm home to supervise.
Hope this helps.
