In E-books, which IIUC this library was designed to parse: very frequently. The ePub3 specification actually specifies the XHTML serialization of HTML5 as its content serialization, so this is a correct eBook. Ironically, this means that most eBooks are not actually valid HTML5. We had another eBook reader (Sigil) that used Gumbo and ran into this issue.

On the web: very rarely. I've actually never seen a self-closing <title /> tag, but I've seen other cases where docs that are actually XML are served with a text/html MIME type and this creates pathological DOM structures.

(I have a funny story from Gumbo's testing that illustrates this. I ran across a document that was actually some XML dialect with 45,000 self-closing elements in a row, but was served with a text/html MIME type. Since HTML5 doesn't recognize self-closing elements that aren't in the spec, this created a DOM tree with 45,000 levels of nesting. Gumbo could handle this because it uses an iterative state machine for parsing, but my testing code did recursive descent on this and choked. I posted it on MemeGen - Google's internal water-cooler website - with a link to the offending web page ... and then got a few emails from other Googlers about how it was kinda rude of me to crash their browsers. It turns out Chrome couldn't handle the page, and would die with a stack overflow when viewing it.)

I encounter self closed <title> tags in malformed XHTML files all the time. In fact I encounter them so often, I used to use a dedicated sanitization pass before passing int he html to html5lib, for that reason alone.