You should do better research.
Jissous don't have anuses, they have cloacas, so shit leaks out without control.
As for the origin, an anonymous on 2chan recieved a plush doll that he had ordered, one that was supposed to be Suiseiseki. However, the doll only vaguely resembled the titular doll.
Jissouseki is the doll that man recieved that day.