Board Thread:Questions and Answers/@comment-46731117-20200826115351/@comment-46731117-20200826124218

Timjer wrote: An owned Asauchi tends to become a Zanpakutō, which lives and dies with its owner. Since most Shinigami manage to turn their Asauchi into a Zanpakutō (even if they're not yet aware of it), and the Gotei 13 probably tries to recover or destroy any lost ones, I doubt many Arrancar or Fullbringers ever get the chance to test out the theory. Remember, the sole ownership of Zanpakutō is the Shinigami's biggest advantage against Hollows and Quincy. I highly doubt any of them would ever want to risk it that others can start using them. Hell, retired Shinigami are even forced to give up their Zanpakutō, further showing how paranoid the Gotei 13 is about their weapons.

This is all true however I was going off the fact that in the Wiki Page for Zanpakutō it says this 

I guess I just assumed that meant all the grunt level Shinigami that we see Ichigo and Gang dispatch easily during the Second Seasom still used Asauchi. I may have been mistaken.

But, for the sake of the Theory, I'd say that it was possible.