extinction (e.g. of a family); dying out; discontinuation
severance (e.g. of relations); rupture; breaking off; (generation) gap
家系の断絶を防ぎたかった。
He wanted to prevent the extinction of the family line.
両国の外交関係が断絶した。
Diplomatic relations between the two countries were severed.
交渉が断絶状態に陥っている。
Negotiations have fallen into a state of deadlock.