Unclosed HTML tags in full post quotes

Sometimes certain members of the community I take part in don’t close their HTML tags. For example, they’ll write a sentence, then use the <small> tag, then write another sentence, without closing the tag at the end with </small>. Obviously this is invalid HTML, but those users don’t know or don’t care.

The problem is, when you quote the whole post using the button in the editor, this copies all of the unclosed HTML tags, meaning everything you type after the [/quote] is affected by this ill-formatted HTML. Is there a reasonable way this could be handled by Discourse so that the tags are closed when doing full post quotes? Feel free to quote this post to see it in action.

Let me know what you think.