From the wikia:
In the DVD commentary for the episode "Shindig," costume designer Shawna Trpcic mentions that the leather necklace Zoë always wears is a symbol of her marriage bond. However, she is seen wearing the necklace in the flashback sequences of "Out of Gas," well before she has married Wash.
Thanks Richard: "In the book Firefly: The Official Companion - Vol. 1, Torres speculates that the necklace is actually a shoelace from the boots that Zoë wore during the Unification War."
I guess I'm just confused why the costume designer wouldn't know what the purpose of part of the costume was. Shouldn't she have known?