Soul Drive (ソウルドライブ, Sōru Doraibu) is an ability that debuted in BS33 together the Sengoku Six Generals. Soul Drives can activate powerful effects, in exchange for removing a player's (Soul Core) from the game. Rather than being restricted to a particular color, it is restricted to Ultimates. Different Soul Drive comes with different timings and conditions, but the most common one is (When Attacks).
The keyword text reads:
While worded as a "By" effect, it is not exactly a "by" effect, but like a "once you xxxx, xxxx" effect. Another thing to note is, you cannot activate Soul Drive by depleting the Ultimate, meaning to send the only core on it, Soul Core in this case, to the Void. On the other hand, the LV of the Ultimate when activating Soul Drive is accounted before actually sending the Soul Core to the Void. Therefore, an ultimate at LV4 can activate its [LV4] Soul Drive even if banishing the Soul Core would bring it down to [LV3].