As the dictionary says, the word “escape” is from the Latin ex, out, and cappa, cape.
In olden days the meaning was literal.
One slipped out of his cape or threw it aside in order to free himself for running, or, it might be, he left it in the clutch of a would-be captor and made away from the spot.
One is reminded of the young man mentioned by St. Mark who, when the servants of the high priests attempted to seize him by the garment he was wearing, “left the linen cloth, and fled from them naked.”
