if both seat stays are sheared off, the bike is not safe to ride. The seat stay connection is not really all that easy, as might be inferred from the fact that it broke on your bike. I used to make spending money in college doing repairs on brake bridges that broke off, I always figured that they had the really drunk guys putting those on in the European factories. Hard to know if that's a repair, it looks like it might be but that joint has seen some weathering so it's difficult to know.