Generally, if the oil remains, it's supposed to be dry. Same when there's a seal, it's typically dry. When wet, there are drains inside the housing, back to the crankcase, and it shouldn't reattain anything more than a small amount of residual oil.
Stators are wet because the oil is meant to cool them. Something like a generator/stator/alternator produces heat. It's typical for a small two cycle engine to use a dry stator, because that's much simpler considering the engine design, and they generally don't have a high electrical output. At times, with a wet stator, there will be a direct oil supply to the housing, to keep oil flowing instead of just splashing around and not removing heat. That's one thing to look for.
It's interesting there is so much confusion about it on a 350X. If it's dry but oil is getting in, the crank seal is bad or the crankcase vent is plugged up and building excess crankcase pressure, forcing oil through the weakest seal first. Also if dry and the vent on the stator housing is plugged up, the temperature cycling could cause spikes in negative and positive pressures, causing oil to leak past the crank seal.
There is a drain passage cast into the case and cover. It's on the lower stator cover bolt area, near the front. It looks like it's to atmosphere, which would mean the stator is supposed to be dry, and that's a tiny drain/vent for accumulated moisture to escape, and also prevent a pressure differential.
The story of three wheels and a man...