The problem was likely caused by the previous owner and the stock jetting, IMO. Over time, the silencer could have gotten saturated with oil due to the extremely rich jetting. So what's spewing out could be what has accumulated over time. There are probably several ounces of oil accumulated in that boat anchor of a silencer.
BTW, the previous owner could have been mixing lots of oil, and using an oil that did not burn completely at the low rpm and temps he was using the bike. The stock plug is too cold, also. Other poor maintenance practices like over oiling the air filter could have made the bike run even richer.
Kawasaki really missed the mark on the jetting for that bike. Even worse than on the 200. On mine, I went down 3 sizes on the main, 3 on the pilot, put in a leaner needle and put in a slide with 1 mm more cutaway.
BTW, my KDX250 tank measured 3.6 gallons, as did my friend's. The manual says 3.3 gallons. A quart of oil per tank would be about 14:1. With proper jetting, even that much oil would not cause a puddle to appear behind the bike.