What exactly is meant by enclosure on the border?

We have purchased a plot of land near Leipzig where the boundary fences are dilapidated and therefore need to be demolished. Now it says on the website amt24.Sachsen.de: "The person who has erected a fence is generally allowed to remove it again at any time, unless something else has been agreed with the neighbor. However, this does not apply to a fence standing on the property boundary if the neighbor has an interest in the continuation of the fence."

Question: what exactly is meant by "a fence standing on the property boundary"? Assuming the fence stands a few centimeters next to the boundary and only the posts have their back on the boundary but not on it. Is that then a "fence standing on the property boundary"?

Thank you very much for your help and best regards

I understand it like this... Normally, you place your fence on your side of the boundary, therefore you built it and of course you are allowed to remove it without your neighbor's consent. Logical. If the fence stands exactly on the boundary because at some point you agreed with the neighbor, you are not allowed to tear it down alone even if you built it. Here the consent of the neighbor will be required...