zi'o removes a place from a selbri's place structure. In doing so, whatever that place contributed to the selbri's meaning becomes irrelevant. For example, a klama fi zi'o goes somewhere, whether or not there is an origin (a te klama). klama fi zi'o describes a relation of going in which the concept of an origin is irrelevant.
When there is no value that could satisfy a given place (i.e. no da broda), the corresponding sentence with zi'o can still be true (i.e. zi'o broda). mi broda no da neither entails nor contradicts mi broda zi'o:
|mi zukte lo ka plipe kei no da|
"I don't jump with any goal."
But do I jump? I might! The following follow-up doesn't contradict the previous statement:
|.i ku'i mi ja'a zukte lo ka plipe kei zi'o|
"But I do jump."
|mi zukte lo ka vofli kei no da|
"I do not fly with any goal."
But do I fly?
|.i ji'a mi na zukte lo ka vofli kei zi'o|
"Also, I'm not flying, period."
Whenever something broda su'o da, it also broda zi'o:
|do sanga su'o da .i ja'o do sanga zi'o|
"You are singing something. Therefore, you are singing."
For practical purposes, zi'o can be used to emphasize that no particular thing(s) are required to fill a certain place as an explicit zi'o prevents the place from being contextually filled by zo'e:
|.au mi tavla do zi'o|
"I just want to talk to you [about nothing in particular]."
"I just want to talk to you [whether or not there's a topic]."