To feign ignorance or pretend not to know (colloquial); to shirk responsibility by acting like you don't know.
問題を指摘されても彼はばっくれて知らん顔をしていた。
Even when the problem was pointed out, he played dumb and looked unconcerned.
店で万引きが見つかりそうになったので、仲間はばっくれて逃げた。
When it looked like the shoplifting would be discovered, his mates slipped away and pretended nothing happened.
To evade duties, slip away, or abscond (colloquial), e.g., ditching work or obligations.
給料日になっても社員が来ず、数人がばっくれて辞めてしまったらしい。
Even on payday some employees didn't show up — it seems a few just bolted and quit.
締切前にばっくれるのは困るから、連絡はちゃんとしてほしい。
It's a problem if you disappear before the deadline, so please keep in touch properly.