A very complex question.
There are several ways in which information can be obtained.
First, the browser itself has access to what it holds. We have no way of preventing this information from existing in the browser.
If your site is exposed to xss then you can run scripts on it.
As a result, you will be able to access the information you have saved at the javascript level, cookies and everything around.
There is another attack that could be in the communication between the site and the "man in the middle" server.
HTTPS communication can help you defend against attack.
Are there other ways?
Probably so, it might be easier to help if we understand the exact challenge you are facing
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