“Ze” (like “they”) is a subject pronoun, it has been suggested with various object pronouns (like “them”), possessive determiners (like “their”) and possessive pronouns (like “theirs”), including at least these patterns: ze/hir/hir/hirs, ze/mer/zer/zers, ze/zir/zir/zirs; ze/zem/zes/zes.

So, the “their” could change to any of “hir”, “mer”, “zir”, or “zes”, depending on which “ze” pattern was used.