Does revoking a sponsor's citizenship also affect a family member who became a citizen through them?

It can, depending on how the family member's own status and citizenship were actually obtained. If a family member's permanent residence or citizenship depended on their relationship to, or sponsorship by, someone whose own citizenship is later revoked for fraud, and the fraud also directly affected the family member's own file or eligibility, that can raise separate questions about the family member's status that need to be looked at specifically.

This is not an automatic chain reaction, however. Each person's situation is generally assessed on its own facts, including what they knew, what was represented in their own application, and whether the fraud in the sponsor's case actually extends to affect the family member's eligibility, rather than the family member's citizenship being automatically cancelled simply because a related person's citizenship was revoked.

Anyone in a family where a sponsor or closely related family member is facing a citizenship revocation proceeding should get their own status reviewed independently and promptly, rather than assuming either that they are entirely unaffected or that their own citizenship is automatically at risk.