User has vendors who don't appear on screens unless they have been changed to the Contract Employee or Outside Consultant vendor type.
This is by design. You can resolve the issue by changing their types to Contract Employee or Outside Consultant. If you don't want to change their types, you also have the option to change your preferences to display vendors along with the employees. To do this, go to User Preferences > General > Fields and Filters and select the option Include vendors in employee drop-downs. Note that vendors don't appear in all screens because you are not meant to manage them.