A Beast-Bonded Witch [LINK] of 10th level gains the ability Twin Soul.
Twin Soul (Su)
At 10th-level, if the witch or her familiar is gravely injured or about to die, the soul of the dying one immediately transfers to the other’s body. The two souls share the surviving body peaceably, can communicate freely, and both retain their ability to think and reason. The host may allow the guest soul to take over the body temporarily or reclaim it as a move action. They can persist in this state indefinitely, or the guest can return to its own body (if available) by touch, transfer into a suitable vessel (such as a clone), or take over another body as if using magic jar (with no receptacle).
The Familiar class feature states:
"The familiar has half the master’s total hit points (not including temporary hit points), rounded down, regardless of its actual Hit Dice."
With that in mind, how many hitpoints does a BBW's (pun intended) familiar have, if its master dies and transfers into its body?
I don't see how the class feature changes anything. I could be wrong but I don't think the familiar's hp total changes just because the master is possessing a body that isn't their own.
If it did change because of this then in your example the familiar/master would have 1 hp. Thanks to the recursive nature of the situation and the fact that the familiar must have a min hp of 1.