In the real world, the father would have arranged (through a will or gifts and/or through private contractual agreements with the creditors) to protect the interests of the son who converted together with the family (regardless of how halacha characterized the relationship). This of course is irrelevant to the legal principles being discussed in the gemarra.
As is common in any legal system in which the full details of actual cases are not reported (i.e. like almost every other legal system in the world other than the Anglo-American system), the discussion of the case in the gemarra focuses on details related to the legal issue being discussed. The real world is always messier with “facts not on point”.