WARNING: The following contains spoilers for My Hero Academia Chapter 334, "Parting Gift” by Kohei Horikoshi, Caleb Cook, and John Hunt, available now in English from Viz Media.
From the beginning, All For One coveted Star and Stripe's omnipotent New Order. He engaged her in battle with one objective: To steal her Quirk and make it his own. Star ended up giving up her Quirk to him but not before rigging it to rebel against all other Quirks. Right after he received it, New Order began tearing Tomura Shigaraki's body apart.
As soon as All For One realized what New Order was doing to his body, he immediately sought to give it away. Trying to pass it to a member of Star's fleet proved ineffective so he fled the battle scene in search of someone else he could grant it to. Desperate and delirious, the first person he ran into was Kashi Kashiko, a convict who'd escaped during the mass prison break and was now attempting to live a quiet life.
Before attempting to pass New Order to him, All For One stole Kashi's Quirk in order to subvert the final rule placed on it. As he transferred it, he was once again placed face to face with Star and Stripe's vestige. It was in a decrepit state after having to contend with the multitude of Quirks All For One held but was conscious enough to inform him that the battle was not yet over. Star's vestige warned that All For One could always be struck down as long as the spirit of heroism that she possessed existed in the world.
Whether or not New Order was completely destroyed or successfully transferred to Kashi is unclear. Star's vestige claimed her rampage had been the death of her in the middle of the transfer process but Star and Stripe's crew members made an interesting note as they were discussing All For One. They made mention of evidence of a struggle where he'd made landfall but that All For One had once again vanished without a trace.
Being the meticulous strategist that he is, All For One must have had good reason for deciding to take Kashi, along with the latter's female companion, when he disappeared. If the New Order transfer was indeed successful, it's unlikely that the Quirk would have power anywhere near the scale of what Star and Stripe could achieve with it. Even so, the thought of All For One in indirect control of such a versatile Quirk is alarming. In this situation, the best case would be New Order being fully destroyed before Kashi could even receive it. Worst case? All For One synthesizing an artificial version without the built-in booby traps for his own use.
Kashi's brief introduction and subsequent disappearance also left his fate quite open-ended. Could the previously small-time criminal have become the most important pawn of All For One's? He never got the chance to display his Quirk and that leaves us to wonder the potential dangers All For One's newest ability may pose.