Some roads have "escape routes" but I can't recall seeing those on mountain passes; I suppose on really bendy sections all it would do is plough you onto the next bit of road. Also; using a sheep to save your breaks, sounds like a plan!!
There are on some French mountain passes, although normally they are just farm tracks off a hairpin. One of my friends brakes failed on his bike coming down a certain Pyrenean mountain, and very fortunately for him the next hairpin had just such an escape track. He wrecked his cleats trying to stop though, and no doubt his cycling shorts (although he didn’t admit this).