ぶじ
safely, peacefully
Everything burnt away to nothing, and a matter to deal with: so no matters at all, which is the entire point. Boo ぶ, gee じ, you are home and the budgie is still alive: ぶじ.
無事に is safely. It means nothing went wrong, not that nothing happened.
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Emaki is not affiliated with, or endorsed by, Kaishi 1.5k or its authors. The word, reading and meaning come from the Kaishi 1.5k deck, used with their permission. The mnemonic, the note and the kanji breakdown are original work, published under CC BY-SA 4.0.