The information in the filed Bankruptcy paperwork is a snapshot of the assets and liabilities of the debtor as of the date of filing.
So as long as the petition and schedules submitted to the Bankruptcy Court are true and accurate at the time they were signed and filed, there are almost no restrictions as to what property a debtor may own or obtain after a Bankruptcy case is filed.
(One notable exception is inheritances, which can become part of the bankruptcy estate for up to 6 months after the date of discharge).
In many cases, a filer will give up a vehicle in which there is a significant amount of debt still due.
So in most cases, yes, a family member may purchase a car to give you after you have filed for bankruptcy. Ownership of a vehicle after making a bankruptcy filing (even if that ownership is taken before the discharge is granted) should not negatively affect one’s bankruptcy case.