There is no "anyone can reissue" option for an asset. But there's a workaround here – before creating the asset, the issuer creates a new address, and makes the private key of that address known to everyone by putting it into the asset metadata. Then after creating the asset it grants issue permissions for that asset to that new address. Now anyone on the chain can add that address (via its private key) to their wallet, and issue more units of the asset as well.
Still I have to wonder why you would do this. Can you explain the use case?