Is plain char usually/always unsigned on non-twos-complement systems?

Obviously the standard says nothing about this, but I'm interested more from a practical/historical standpoint: did systems with non-twos-complement arithmetic use a plain char type that's unsigned? Otherwise you have potentially all sorts of weirdness, like two representations for the null terminator, and the inability to represent all "byte" values in char. Do/did systems this weird really exist?