My 8 yr old just had this happen. He has had diarrhea issues his entire life, but never this. It is called a prolapsed anus, and even if it resolves in its own, u need to go to vet for antibiotics and to discuss possible causes. It’s not normal, but can happen when straining.
Basenji puppies can really be a handful for those who are unprepared for it. I think girls are generally better behaved than the boys. No surprise! All Basenjis are different, but as the mom of an 8 yr old blind male (bad breeder, he has PRA), our experience with Bongo (from 11 wks to about 18-24 mos.), was that he was a total sweetheart who had an appetite for secret destruction! This adorable little baby chewed holes in every single piece of furniture in our living room. AND we had a crate. He would do it when I was around but not looking at him! My husband had this v expensive sculpture and one day I came home to find Bongo up on a console table delicately biting and licking the most expensive thing in our house!
We had some trying times for sure. But he has taught our family so much. We all love him so much. Basenjis are aristocrats and they LOVE to be naughty. Give your new girl lots of exercise, use the crate, and teach her the rules. Even if she won’t always follow those rules, make sure she knows them. I think Basenjis are the most lovable creatures I’ve ever had the privilege to know.