Is missing a common noun or proper noun?

The Word (gerund) 'missing' is a common noun, a general Word for a person or thing that can't be found.

A proper noun is the name of a specific person, place, or thing. Examples of proper nouns for the common noun 'missing' are "The Missing" (2014 TV mini-series) or the National Center for Missing & Exploited Children (non-profit organization).