The cob or other earthen plaster incorporates clay or livestock manure which add hydrophobic and polymeric properties, which then air-cures to seal out moisture, and it’s thick so if it gets wet it has to get really wet to penetrate the hay. Ideally these also have large overhanging rooves to sheet away rain.

I’d be more worried about fire. High temperature plus a bit of moisture from, say, a leak, will cause hay piles to spontaneously combust.