Dear @shino_mikaka, welcome to the Box Community!
You're correct in that Box (and similar cloud services) typically logs file access when the file is opened or modified, especially if there's an internet connection at that time. However, if the file is accessed offline, those actions might not be immediately visible in the history logs until the device syncs when it reconnects to the internet.
It’s really a challenge to track offline file access, but a combination of device encryption and other security strategies can help mitigate the risk. You can’t rely solely on the Box history logs for offline access, so implementing additional security controls and planning ahead for lost devices can provide some protection.
Also if possible, you might want to limit the types of files you take offline. For example, only take certain files offline that are of lesser sensitivity.
To discuss security strategies and other features that can help secure your content with Box, I highly recommend getting in touch with your Account Executive and Customer Success Manager. I’ve sent you additional information regarding this.
Please let us know if you have any other concerns. 
Dear @Jey Bueno Box,
Thank you for your detailed response and suggestions.
I also serve as Account Executive and Customer Success Manager. The ultimate purpose is to identify the extent of information leakage when a device is lost.
Since it remains in the history when the file is opened, I thought that it might remain in the history even when offline processing (caching) is done, so I decided to post it.
Is it correct to assume that when offline processing (caching) is performed on a tablet such as an iPad while connected and accessing BOX, the history will not be retained?