To Escape Something
To Avoid Something
transitive verb, ichidan verb
You are going to excuse yourself from the situation, and in order to do that, you have to escape from the person / thing trying to hold you there in order to avoid them.
まぬかれる
まぬがれる
In order to do that, you jump inside your man(u) car (まぬか) which is a car for a tough man(u) that needs to drive fast, just like you.
倒産という最悪の結末だけは何とか免れることができた。
We managed to avoid the worst possible outcome of bankruptcy.
死刑執行を免れるためなら何でもします。
I'll do anything to escape execution.
後部座席に座ってシートベルトを締めていたので、私達は重傷を免れました。
We avoided serious injury because we sat in the back seat and wore our seat belts.