If you have a Secured Work Template, then it will not apply to any other Fragments that might be contained in it. 

This Inspection Work Template is a Secured Template. 

It has a "Waste Dump Location" Group Fragment Template. This is represented by the "star" symbol. 

The name of the Fragment Template is "Group Waste Dumps - Inspection". 

If you navigate to the Fragment Template itself, you will notice that it does not have a "Secured Template" marker. 

A user with Work Templates Admin permission can edit this Fragment Template. To summarise, Secured Templates with Fragment Templates will be editable. You will need to add the Fragment Template to the Template Group as well. 

What happens if Fragment Templates are in Secured Work Templates