To stop contacting someone / to cut off communication; to lose contact or become unreachable.
彼は突然家族と連絡を絶った。
He suddenly cut off contact with his family.
台風の影響で山間部の村としばらく連絡を絶っている。
Because of the typhoon, we've been out of contact with the mountain village for a while.
彼女は昔の恋人と完全に連絡を絶ったと言った。
She said she had completely cut off contact with her ex.