This happened to me, once, with a 1982 BMW R100/7. It was on the center stand, on level ground, shrouded in an appropriately sized cover. After a storm one night, I emerged to find the bike tipped over. The left cylinder head was cracked. This was no big deal, as that was a $40 part back then and attached with three screws. Even I could fix it.
I would characterize that bike as a bit top heavy, though, especially mounted on the center stand.
It is still in my step-Dad's garage. Been there for 18 years. I should dig it out.