You can steal and make a copy of the HTML and other code that is delivered to the web browser. If only that is stored on the web server you can make a copy of the website, at least all of it you have access too. If you need to log in what you have access to often is in part specific for you. You can access for example access my Reddit chats

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The problem is most website is not made by just static HTML files stored on a web server. Reddit, for example, uses phyton code that is executed on the server, and it access databases with all the post, comment, user preferences, etc that are used to create the HTML pages you get and your browser display right now. The website does not give you direct access to the phyton code or the database when you browse the website.

So making an exact copy is not as easy as it first looks like.

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Nothing says the code that generates the website can be published too, you do not need to but it looks like at least part of Reddit is available at https://github.com/reddit I am not sure what is included and if it is complete or not. But I doubt that Reddit provides a public copy of the database.