Repeated unwanted contact that communicates a threat is called

Repeated unwanted contact that communicates a threat is called STALKING.

Explanation:

Stalking is said to occur when an individual, who has no reason to contact one, begins to monitor and follow one around. This situation is also called HARASSMENT. It involves continuous bothering of another person, even after the person has indicated that he will prefer to be left alone.

Stalking usually makes one to be afraid and to feel unsafe. Stalking can involve individuals, families or friends.

Stalking is a criminal offence that is punishable under law and anyone who is experiencing such have to report the case to the nearest police station.

Stalking behaviors include: constant communication through phone calling, internet or texts, constant following, constant watching of one's house, leaving threatening messages, etc.