To manage to escape to safety; to get away and survive or reach a safe place.
住民たちは津波の予兆で高台へ逃げ延びた。
The residents escaped to higher ground in time and survived the tsunami warning.
彼は逮捕を免れて、国外へ逃げ延びたと言われている。
He is said to have avoided arrest and fled the country to safety.
森の中を走って、ようやく村まで逃げ延びた。
He ran through the forest and finally made it to the village safely.