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The correct understanding of the situation with cached data on a shared iPad when a user logs out is that the data becomes inaccessible until the next login. When a user logs out of a shared iPad, the cached data associated with that user account does not get deleted immediately. Instead, it is retained on the device, meaning that it is still stored locally but is not accessible to other users until that specific account logs back in. This feature is designed to allow users to pick up where they left off without losing their information upon logging out, while preventing other users from accessing that data.

The option suggesting that the data is retained locally and synced to iCloud inaccurately implies that there is automatic syncing of that cached data to iCloud upon logout, which isn't a standard behavior for shared environments. The data's status changes to inaccessible, not permanently stored or erased. Thus, the framework of shared iPads emphasizes user privacy and data segregation by retaining personal cached data until the user returns, safeguarding it from other users.