I’ve been storing my shotgun ‘barrels
down’ for several years. Years ago I bought a pre-owned Perazzi TMX w/a lot of oil soaked into the stock that looked like it was there for years. After some time, the oil dissipated from the stock through gravity.
Some folks, my Dad for example, preserved his farm tools in old motor oil. His habit of using plenty of (gun) oil to clean his guns carried over from his tool cleaning habit. I don’t recall that he stained his gunstocks, but it could have happened.