Why would a agency keep maintaining my backlinks if I leave them?

As grumpyseoguy says the correct way to provide backlinks for customers from an agency would be to have a PBN (not network but I forgot the other wording) and that would mean that the agency owns the websites. My question is why would the an agency maintain and keep my backlinks on their websites even after I stop doing SEO with them?

To me it seems like as soon as I stop working with a agency they have the power to remove everything and it would be better for them to do so since they would not have to maintain the backlinks and my rankings would drop which will make me think that I was doing better when I was with them. Also do you think it is better if an agency tell you that they are buying links from another party or that they are building the links themselves?

What do you think about this?