entire family affected; whole family wiped out
Used when a disease, disaster, or tragedy affects or kills every member of a family. Often carries a grave or dramatic tone.
There are cases where an entire family was wiped out by that infectious disease.
The tragedy of a whole family being wiped out occurred during the war.
全滅 means total annihilation or complete destruction in general, while 一家全滅 specifically refers to the entire family being affected or killed.
Compound of 一家 (one family) and 全滅 (total annihilation). The exact historical derivation is uncertain, but the meaning is transparent from its components.