To flee or abscond (often secretly leaving home, workplace, or eloping). A somewhat literary/old-fashioned term.
彼は給与の未払いを理由に会社を出奔した。
He absconded from the company citing unpaid wages.
両親に内緒で彼女と出奔する若い二人がいた。
There were two young people who eloped together without their parents' knowledge.
その政治家は汚職疑惑が出るとすぐに出奔したという噂がある。
There are rumors that the politician fled as soon as the corruption allegations surfaced.