Boundary fences usually belong to either one property or the other. Where there are fence posts to one side of the boards, rather than being in the centre, the convention is that a fences is erected with the owner having the posts on his/her side of it. (NB: That's only a convention. It's not a 'rule' or 'law' but it can help to work out who actually owns a fence).
If a fence falls into disrepair then (unless there's a covenant in force requiring the owner to maintain the fence), the owner is at liberty to
(a) leave it as it is ; or
(b) repair it ; or
(c) replace it ; or
(d) simply remove it altogether. (If the owner of the adjacent property thinks that there ought to be a fence along the boundary, he/she will then have to provide one at their own expense).
So, in order to answer your question, it's necessary to understand who actually owned the old fence. Assuming that it was your neighbour, he/she was entitled to do whatever they wanted with it. If the fence was yours, your neighbour should have either left you to deal with the problem of its repair or, at least, consulted you prior to taking action on his/her own.