to avoid or shirk responsibility; to try not to accept responsibility for something (often has negative connotation).
問題が起きると彼はいつも責任を避ける。
When a problem occurs he always avoids responsibility.
リーダーが責任を避けるのは信頼を失う原因になる。
A leader avoiding responsibility can be a cause of losing trust.
その部署は責任を避けるために事実を隠していたと非難された。
The department was criticized for hiding facts to avoid responsibility.