If the fence looks like it is going to straddle a property line, you and neighbor should jointly order an updated property survey to determine EXACTLY where the property line is.
If the neighbor's fence touches your property in any way, you should send a certified letter to that property owner that you are, in no way, ceding any part of your property to him/her/them. (This is simply a matter of law, and not an effort to be disagreeable or confrontational, but you do have to keep everything straight, especially if you don't plan to own your property forever.)
If someone's encroachment on another's property is allowed to exist long enough, the law might regard it as you having given permission to occupy and eventually own that portion of your property, simply because of the passage of time.
CHECK WITH A REAL ESTATE LAWYER WHO CAN ADVISE YOU ABOUT HOW THE LAWS AND COURTS IN YOUR STATE REGARD SHARED FENCES AND ENCROACHMENTS !!