I have seen this happen on several small air-cooled mower engines and such and one car engine.
Here is what happens. I am given a non-running mower or find one out at the curb on trash day. I pick it up and realize that the problem is something simple like needing a new spark plug or the carb has been gummed up with varnish from sitting over the winter without stabilizer.
Of course I change the oil if I can get one of these running. A few have had oil that resembles black ketchup rather than oil. I have had to try and get this out of the drain hole with a screwdriver, then top off with fresh oil to do another rinse. I then usually run another rinse of good oil and hopefully it will come out clean by then.
The odd thing is that usually the engine will seem to run fine on the sludgy oil without smoke and such. As soon as I put good new oil in the engine, things start to go bad. Massive oil burning and smoke that gets worse the more I change the oil is not unusual. Then, the rod often comes through the block. While these engines were neglected and not going to last, it seems that putting fresh oil in them hastens their demise. Has anyone else seen this and what is the explanation? I figure the bearings and such are so worn from neglect that the thick goo cushions them. I also figure that the oil is too thick to be pushed past the rings.
I know people who run mowers for years by just adding oil as needed. They never change it. While I would never do this, it seems like it works for a lot of people and that changing oil in one like this may actually not be the best idea.