By default, lists have no shared document web space. Thus, you need to create it. To do that, go to the list administration module and click on the 'Create shared' link.
To allow subscribers to publish documents in the shared document web space, you need to change default rights: in the list administration module, click on 'Edit list config' and then on 'Privileges'. At the bottom of the page, there is a drop-down list entitled 'Who can edit'; choose the 'Restricted to subscribers (private)' option.
Be careful: if you created folders before changing those rights, the folders will still be unwritable. If you want to make them writable, you will have to change access rights for each folder.
You might also want to set up quotas for the shared document web space on the 'Privileges' page of the 'Edit list config' section.
To know everything about the management of the shared document web space (how to organize it, change access rights, name documents, etc.), refer to the 'Using the shared document web space' section of the User guide.
To deny access to the shared document web space, click on 'Delete shared' in the 'Admin' submenu. Then you will still have the possibility to reopen it by clicking on 'Restore shared'. Deleting and restoring the shared document web space has no impact on the documents it contains.