Extra water line under sink?
Thank you for asking. And yes absolutely, it could be/could've been for a refrigerator, dishwasher, humidifier, poorly and illegally done toilet, standalone ice maker or even a trap wetter for a basement floor drain.

It was done by someone for a reason, so you should find out exactly what that reason was/is...since you now know where its local shutoff is in the case of service or emergency.

Only if you can pull the hose all of the way out to find its not connected at all should you cap it or change to a regular shutoff valve. If you don't need it and it's not currently doing anything, then go ahead and delete it.