Thanks for the information. One of three scenarios seems to have occurred.
1.) The puppy has hydrocephalus while still in utero at the stage of development where the membrane forms around the brain and the skull bones fuse. Hydrocephalus literally means "water in the brain" where intracranial pressure builds up because the drainage apparati of the brain get blocked.
2.) There may have been a congenital malformation that primarily prevented proper skull bone formation and even a normal brain never had a chance.
3.) Megaencephaly may have occurred that prevented proper skull bone fusion. Megaencephaly literally means (big brain), and refers to a congenital condition where the brain develops at a size that is too large.
Since none of these possibilities are considered a breed linked problem in Basenjis, this was likely a genetic abhorration, not something that was necessarily inherited from mom or dad. These types of abhorrations tend to occur with increasing frequency as breeding females reach middle age.
The good news is that this issue was likely linked only to this puppy, and will not likely impact the other puppy (ies), as this occurred within this puppy's own developmental embryonic sac.
I do not think that necropsy would be of any value in this situation, as "congenital malformation" is pretty obvious just fro the history you provided. A DNA analysis for genetic disease inherited from mom or dad probably would also be of little use, as these are considered breed linked disease in this breed. As such, I would just do little more than focus on the health of Mom and the puppies that are viable.
Regarding mom, I never just rely on abdominal palpation to determine if there are puppies left in the uterus. I have been practicing for 11 years and am very comfortable with palpation...and have missed puppies that I discovered once x-ray or ultrasound were done. The implications of a puppy stuck in utero too long can be fatal for the puppy, as well as make mom very sick.
As such, I advise an abdominal x-ray or ultrasound, preferably ultrasound if your vet does it. With a congenitally malformed pup and a slow propagation through the birth canal with puppy number 2, I would also have a calcium level checked. Calcium can drop precipitously even under normal labor, and can become troublingly low after any difficult birth. Since calcium plays a pivotal role in muscle contraction, low calcium can adversely affect the heart muscle and cause dangerous arrhythmias of the heart (not to mention weakness, labored breathing, vascular problems, and decreased milk production).
If a congenital still born puppy occurs again with Tine, I would advise retiring her from breeding and having her spayed. I generally advise retiring any breeding female from breeding by 5 years regardless of her history, as things tend to go wrong after that time, both with puppies and mom.