More help for your parents, they shoul dnot underestimate this as such behaviour is akin to stalking.
Mobile phones are a popular choice for bullies. They provide bullies with the perfect means of taunting their target with little fear of being caught. Text messages provide complete anonymity.
Many pay-as-you-go mobile phones can be bought over the counter and do not require proof of identity, nor is any record kept of the new owner. Calls made from these types of mobile phone are difficult to trace.
So, what can you do?
Never ignore or underestimate the threat
NEVER ignore threats, either verbal or by phone or via text message. But don't respond in the way the bully wants you to. When people advise you to "just ignore it", what they really mean is "do not respond to the taunts and provocation, do not engage or communicate with the bully, but instead take careful notes of what is being done to you, who is doing it and how, and record all of this in a journal so you can develop a strategy for dealing with it". The golden rule is, DO NOT RESPOND and DO NOT ENGAGE. You have a right to not respond to abusive people.
DO NOT UNDERESTIMATE the distress and the destructive effect that constant bullying and harassment can have on the recipient and their family. Bullying in all its forms invades your boundaries, is intrusive and violational and is thus a form of rape - emotional rape and psychological rape - especially when this goes on for months, or even years.
Empower yourself with knowledge
Understand what bullying is so that when it starts you can stay in control and nip it in the bud. Do your homework now. Start by digesting this page, then follow the links.
Recognise it early and keep records
Learn to recognise the early signs and keep a detailed diary. Print off the messages if you are able, otherwise make a careful copy of every one (including formats, abbreviations, spelling mistakes etc), the date, time, the caller-ID if available, or the reason for the caller-ID being unavailable (eg "withheld", "unavailable", etc) - even this can prove useful. It may be distressing to make a copy of each message, so get the support of a trusted friend or close family member.
Stay in control
This is a game - a nasty game, but a game. Learn the rules of the game: it's about power and control. Tell yourself repeatedly that the threats, insults, accusations, allegations, criticisms etc have NOTHING WHATSOEVER to do with you - they are a device for taunting, a fabrication, a deception, but most of all, a projection of the bully's own weaknesses, shortcomings, and failings. Every nasty word is an admission by the bully about themselves.
Detach yourself from the harassment early on. Each time you receive a message, train yourself to NOT think "what have I done now?" or "in what way is s/he telling me I'm useless this time?" but instead THINK "what is this jerk revealing about themselves this time?" The criticisms, allegations, insults, threats etc sometimes contain a grain of truth which is there to fool you into thinking that the insult has validity WHICH IT DOES NOT. Don't be fooled by this ruse.
Understand the bully's mindset
Bullies derive gratification - a perverse sense of satisfaction - from the power and control they exert over their victim. The aim of bullies is power, control, domination and subjugation. Bullies confirm the power and control by use of provocation. When the target responds, it's a sign that the bully has successfully exerted control. They jerk your string, you jump. By refusing to jump, you deny the bully their sense of satisfaction.
Bullies are also serial attention-seekers. They want a response - they don't care whether it's positive or negative, they just want your attention. It's like a 2-year-old throwing a tantrum. In fact, the harasser may have the emotional development level of a 2-year-old. When you don't respond, the harassment is at first likely to get worse as the bully is denied the fix they obtain from confirmation that they have controlled you (ie provoked you into responding). Choosing to not respond to provocation is more difficult than it sounds.
Get help and support
It's difficult to handle bullying by yourself, even if you're an adult. Text message bullying is similar to stalking. The bullies, who operate outside social norms, will try to isolate and separate you from friends and family, but don't be fooled.
Contact your telecommunications service provider and ask their abusive calls helpdesk for advice and assistance.