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I am very sorry you are dealing with this situation. A prescriptive easement may be a legal theory in which to seek recourse. Unfortunately, even if the cable company was wrong in removing the cable they are unlikely to admit it was there fault and unlikely to address the issue and resolve it without being forced to do so by a court order. In other words, even if the cable company wrongfully removed the cable, you will have to initiate a lawsuit to either negotiate a settlement or have your day in court. This puts them in the position to defend themselves in which they may decide to reinstall the cable at no expense to you to avoid the high cost of litigating the matter with the risk of losing.
It is unfortunate when a person is wronged it takes going to court to resolve the situation but often as in this case there is likely no other means to resolve the issue. You could attempt to file a consumer complaint with your State Attorney General, this could result in the consumer protection division intervening and assisting you with getting the cable reinstalled. In addition, a consumer complaint could be filed with the FTC as well.
I know this was not what you want to hear.
All my best and encouragement.
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Please be aware that the information provided here is not legal advice. Rather it is simply general information. All states have intricacies in their laws and any information given is simply information only and specifically is not intended to be, nor does it constitute, legal advice. This communication does not establish an attorney-client relationship with you.