Documents assigned to different objects inherit the access of these superordinate objects by default. Access to the parent object can be restricted by profiles etc. Access to assigned documents is controlled via the global access flag (Global) of the document data record.
Document access
Globally usable documents of objects with restricted access
If you assign a new or existing document to an access-restricted object (process, contact) that can be used not only for this object but “globally”, the Global flag must be checked for this document and set if necessary. Only then can other users continue to access the document, even though it has been assigned to an access-restricted object.

Global flag at documents
Important note: In addition, a document set to Global, e.g. a customer logo etc., prevents such already checked-in standard attachments from being treated as duplicates again and again during e-mail import.