CB Gallery could be used to store the documents I suppose. You'd then just protect access to it using CBSubs and CB Privacy. This could be displayed directly on their profile.

First you'd want to create a tab for the gallery in CB > Tab Management; lets just call it Documents for this examples sake. Now within that tab under Integrations > CB Privacy set its privacy to forced privacy controls then set the default to private. This ensures only the profile owner and CB Moderators can access the tab. Now under CBSubs Fields Tabs Protection protect the tab with your plan so the profile owner can only access the tab if they're subscribed.

Ok, that covers our tab needs. Now you'll need to create a Gallery field on that Documents tab. Use the below parameters for best display.

Global
Show on Profile: Yes, 1 line without title
Show on Registration: No
Show on Profile Edit: No
Parameters > Display
Asset: documents.[user_id]
Parameters > Display > Albums
Albums: Disable
Parameters > Display > Photos
Photos: Disable
Parameters > Display > Videos
Videos: Disable
Parameters > Display > Files > Create
Access: SELECT_CB_MODERATOR_VIEWACCESSLEVEL_HERE
Parameters > Display > Music
Music: Disable

The above should give you a gallery that only accepts files and can only be uploaded to if the user is a CB Moderator due to the create access limits. The Asset ensures it's a unique gallery tried to each individual user. You'll be able to upload their documents directly on their profile. Technically you could also just use a bunch of File fields on that tab if you like.