That's the crankcase breather. Normally there will be a small amount of "blow by" gas (combustion gas that has gotten past the piston rings) which is a combination of combustion gas that mixes with and picks up oil mist from the crank case. The more wear an engine has is indicated by increased blow by. Engines that have not been maintained well or have excessive wear will collect a small amount of oil in the upper part of the breather and then the blow by gas will push that oil out when the engine is running.
In general what is shown in the photo looks like a lack of or poor maintanence along with engine wear. An engine with a lot of blow by "may" run that way for a long time, but will use engine oil, on the other hand, depending on the severity of the blow by the engine could be on its last leg too.
In a engine with little wear, there should be virtually no oil in the breather and no oil running out of it, just a little vapor coming from the breather.
Ditech-