All engines stay full of coolant (which is hot and pressurized when you turn an engine off), and when you turn off a Subaru engine, the oil drains into the oil pan but more slowly than it would in an inline engine.
The bottom cylinders in WWII era radial airplane engines did fill up with fuel when the planes sat, but that was an earlier design
Subaru did not have widespread gasket problems with its EJ20 or EJ22 engines because the cylinders were smaller in inside diameter (and thicker) and each cylinder made less power during combustion. Likewise, the 6 cylinder engines, all semi-closed deck engines (the turbo blocks), and the new FA/FB engines do not seem to be much of a problem with regard to head gaskets. The FB engine is still open-ish deck but because the bore is MUCH smaller (with a longer stroke) the cylinders are thicker.
I do recall reading that leaky Subaru batteries somehow make the coolant more acidic somehow, and that kind of thing might be an issue, but the simple example of the EJ22 not having HG problems and the EJ25 having them for its whole life shows a weak design point. I believe it would have been cheaper for Subaru to use semi-closed blocks on the normally aspirated EJ25's in the long run, despite the higher initial cost.
Here's an article with some photos that show open vs semi-closed deck blocks:
Our Blogs Technical Articles Subaru Closed Deck vs Open Deck blocks