The ability to delete records in Salesforce is controlled by the role hierarchy. Setting a sharing model to "Public Read/Write" alone does not give users the permissions to delete other users' records.
Any other User trying to delete a record will receive an 'Insufficient Privileges' error.
Users below you in the role hierarchy may have read/write privileges via sharing model rules. However, they may not delete records owned by individuals above them in the hierarchy.
See also
User Role Hierarchy
Considerations for Deactivating Users
Object Permissions
Who Sees What: Record Access Via Roles
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