In Yoshi's Island, the score awarded at the end of a level includes stars, which are analogous to Yoshi's health meter (if he runs out, Baby Mario is kidnapped), but recover automatically over time as long as Baby Mario is on Yoshi's back.
Due to the automatic recovery, it is only possible to get 0 points if Yoshi finishes a level by waiting until his star counter runs out, instantly retrieving Baby Mario and finishing the level, which is only possible if there are enemies in the final room of the level (as he cannot change rooms without Baby Mario, and getting him back in another room will cause the stars to start recovering by the time the goal is reached).
As such, the only worlds in the game where it is possible to get a 0 point total are World 2 (seen in the screenshot in the GBA version) and World 6, since in all others there is at least one level with no enemies in the final room, making it impossible.
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