A dust collector is disclosed for use with a drill bit or a depth stop that is coupled to a drill bit. The dust collector includes a rear attachment portion configured to be axially fixed to a drill bit or to a drill bit depth stop that is axially fixed to a drill bit. An intermediate non-collapsible portion is attached to a front end of the rear attachment portion. The intermediate non-collapsible portion defines a dust-collecting pocket and is structured to inhibit collapse as the drill bit is inserted into a workpiece. A front collapsible portion is attached to a front end of the intermediate non-collapsible portion and at least partially collapses as the drill bit is inserted into a workpiece.