In Three Kingdoms, there is a common, almost casual discussion of wiping out whole families. E.g., the downfall of the Ten Eunuchs also means that their whole clans are wiped out, etc.
Is this really what happened in Late Han China? (It seems like a Mongolian policy, so it doesn't seem impossible that Luo Guanzhong living in the Yaun dynasty might have imported it from his present, but it does seem pretty unlikely that it would have been inserted as a blatant anachronism.) If so, was this official, legal policy, or was it just a course of action habitually taken by powerful lords using their personal influence to execute rival families extrajudicially (even family members not accused of any crime)?
If this was official, legal policy, how far did it go? Was it only for political crimes, or would it apply to common criminality as well? I assume that having a common pickpocket in the family didn't justify killing everyone in the family -- did it? Would a person convicted of some non-political homicide (e.g., a man who kills his neighbor after repeated arguments over property disputes) take his family down with him?
The origin of this policy came before Han, around Qin Kingdom, which made the legalistic policy that all citizens were obligated to report crimes of their neighbors and their families.
Communities are organized into units of 10 households, if 1 person commits a crime, and the other 9 households do not inform their knowledge of the crime to the authorities, all 10 households would be punished equally as if they all committed the same crime.
The policy you referred to, is the Execution of a clan within 9 degrees of relations by blood. (9 degrees is generally considered back in ancient times as the limit of clans).
This was generally only reserved for the most heinous crimes, usually for political betrayal of one's Lords. (by assassination, plots, etc.)
Personal crimes are generally not punished that severely.
Smaller degrees of political crimes, (not very flattering criticisms), may have lesser execution of the clan (within 5-8th degree of blood relations, for example).