I have had 2 similar incidences in my life:
1) A girl from high school tracked me down after I moved to Dallas for college. She started calling me 10-15 times per day... I rejected her politely, then more directly (again & again & again). The calls kept coming. I got really weirded out (this was not long after the movie Fatal Attraction had been out). I called the phone company & explained the situation & they issued me a new, unlisted number at no charge. I later heard that this girl was obsessed with me and a couple of other guys... she committed suicide not long afterwards.
2) Last year I started getting calls that Caller ID said were from a nearby hospital. The caller left several messages saying that he had (girls name), and he was trying to take care of her, but if I didn't get him the money he didn't think he would be able to keep her alive (said in a menacing voice). After getting a couple of these messages, I called the police to report it. They said they would investigate & get back to me. He called later that same day... I answered & he angrily asked if I had received his messages. I said yes, and that the police knew all about him & would be with him directly. He hung up & I never heard from him again. The police called later to say there were no missing persons reports that matched the situation, that it is very easy for a hacker to change the caller ID tag on their phone to say whatever they want it to say. Weird stuff.