Please see https://www.mediawiki.org/wiki/How_to_report_a_bug and provide a link where such a problem can be seen.

Sounds related to the parser? I'm sure an existing bug around balanced templates exists?

It would be better to use ExtensionTemplateStyles to target .mw-parser-output to have this effect, rather than emit unbalanced tags in wikitext. Dunno if that's possible... but it should be.

In theory T114432: [RFC] Heredoc arguments for templates (aka "hygienic" or "long" arguments) would let you do something like:

{{archived page|<<<

at the top of the page and

>>>}}

at the bottom of the page, with no other changes to the content necessary. Assuming something like T114445: [RFC] Balanced templates, that would also ensure no open tags leak out.

I'm a bit surprised that Remex isn't closing the open <div> at the end of the mw-parser-output. That's probably a bug or othersight somewhere. I've been doing that work as part of T198214: Deprecate and remove non-remex Tidy modes of the core parser; it's possible in fact that https://gerrit.wikimedia.org/r/469882 would fix it.

TemplateStyles affects blocks inside .mw-parser-output, but does not directly affect .mw-parser-output. Affect the entire page instead of part of the page may be against "Template"Styles goals.

In heredoc way, the parameter 1 will be filled in the templates, which means that the limit of template expand size will be quickly reached.

Expecting a balanced page, with a closing div or heredoc close is incompatible with what is probably the primary use case. If someone uses the new-section button, or casually adds a new content or a new section at the bottom, the closing div will no longer be at the bottom. Not only will that mess up the rendering of the page, but the closing-div may get automatically archived. Archiving would again result in a page with an unclosed div.

All open tags need to be auto-closed at the end of parser output. Anyone who expects tags to always be balanced is working at the wrong website. We're a wiki, and wikitext should not be mistaken for HTML or treated as HTML. We EXPECT clueless or semi-clueless users to put in arbitrary/malformed content, and wikitext is supposed to be more user friendly than HTML.