Your neighbour likely doesn’t have to build their own fence if they don’t want to. Except in a few specific situations, no one has to build a fence. There is no general law requiring a fence between neighbouring properties; most people simply agree to have one.
When someone enters your property without permission, it’s called trespassing. For example, if your fence was on or just inside your property line, and your neighbour entered your enclosed land without your consent, this would be trespassing. This is because under the law in BC, a person found inside enclosed land without the consent of the owner, lessee or occupier is a trespasser.
Practically speaking, if your fence is six inches inside your property line, it may be difficult to stop your neighbour from crossing over the property line. Legally speaking, the definition of “enclosed land” includes unfenced land that is posted with signs prohibiting trespass. While putting up signs may be a legal solution, this would likely impact the relationship you have with your neighbour. You may want to talk with your neighbour to explain the facts to them, let them know what your concerns are, and try to reach a common understanding. For example, your neighbour may not realize you have built the fence six inches into your property line, and may be happy not to use that strip of land once they learn it is yours.
You may find our page on fences and neighbours helpful. In particular, see the section "Work out problems."