Repeated, unwanted contact that communicates a threat or makes someone fearful can be referred to as

The series of actions like repeated and unwanted contact that makes some fearful can be referred to as stalking.

Explanation:

The term stalking is defined as unwanted or repeated surveillance aimed at an individual either in a direct or indirect way. It is like following them everywhere, sending gifts, making texts and phone calls, gathering information about them, threatening them verbal.

And, in rare cases, harassing the whole family of the individual even after complete disapproval of their behavior. This persistent unwanted approach makes the victim to be in constant fear and also can cause an emotional stress. Stalking someone is a criminal offence in many countries.