Fences constructed on the boundary line between two properties – as most fences are – are owned equally by the two property owners, and both are equally responsible for the fence maintenance, repair and replacement, i.e., 50% each, unless one owner was more responsible than the other for necessitating the needed action, in which case the financial responsibility of the owners is proportional to their responsibility in causing the need.
If you neighbor refuses to accept financial responsibility, you can send him/her a letter (by registered mail, return receipt requested, or by fax – to have a record that the neighbor actually got the letter) detailing the refusal and stating your intention to proceed with the work, to pay the entire cost yourself, and then to recover the amount of his/her share of the cost in small claims court.
In the instance where the fence is not exactly on the boundary line, the party whose land is “taken” can call for relocation of the fence to the property line. It will probably be necessary to have a surveyor stake the boundary line as it is described in the deeds of the parties. In all but the rarest instances, the fact that the fence stood off the property line for many years, or even that there was an agreement between prior property owners that the boundary line would be where the fence is, does not change the true legal boundary line from the location fixed by the surveyed line described in the deeds of the parties.