That constant radius curved end is a clue. Is it hard plastic? Does the open end appear that it has never been attached to anything (e.g., no deformation from a clamp or barb or change in diameter)?

It could be a vent for the differential. One end attaches to the diff. The tube then goes upward, ending in that 180* u-turn so the open end is facing downward so nothing falls in.

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2001 X5 3.0i, 203k miles, AT, owned since 2014