If your files & attachments are related to the Case Email, then you can download them from the Email Message.
Follow the steps below to download files & attachments from "Email Message" in bulk.
1. Open the "Mass File Download" Tab and Click on "Related Files & Attachments."
2. Now select the "Email Message" form, Select Object drop-down
3. Select Advanced Search (SOQL) search mode and write a query based on your search criteria. You can try this as well to search all the case records - ParentId IN (SELECT Id FROM Case)
4. Click the Search Button
5. Now click the Download Files & Attachments button and download up to 2000 files at one time, and then another 2000 files, and so on
PS: View Mass File Download, Salesforce file download app on Salesforce AppExchange: https://appexchange.salesforce.com/appxListingDetail?listingId=a0N3A00000EcsAOUAZ