How are segments linked to their parent list?

Segments are chunks of filtered subscribers based on a rule you have applied. In that sense, segments cannot be created individually and independently from the Contact List you've based them off.

You can use the segments individually to send email campaigns to without affecting the whole list of subscribers but you cannot remove the people from that segment from the main list.

This is because the segmented subscribers are still part of the main contact list - the only difference is that these contacts are filtered out based on a rule you've created so you can target this particular group of subscribers independently from the rest of your recipients in the same list.

You can export, edit and delete a segment with individuals without affecting their status in the main list.