This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
萙 is a rare character whose historical development is uncertain. It visually combines the grass radical 艹 with 枕, but the exact origin is unclear.
The grass radical 艹 sits above 枕 (pillow), like grass growing over a forgotten pillow. This image can suggest tiredness or weariness, but the meaning is not firmly established.
For くたびれる, imagine a pillow (枕) under the grass (艹) that makes you so tired you collapse: 'kutabire' sounds like 'coot-a-beer' — after a long day, you're too tired even for a beer. くたびれる.
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