Earlier quoted context omitted.
There was - it was called LiveConnect - but like most things to do with Java and the browser(s), it languished in a half-supported state, and really isn't worth thinking about any more. As are applets - a great idea, implemented poorly, and now essentially lost to the annals of history.
Don't forget about websites from academia that implement certain proof-of-concepts; for some reason that commumity still keeps using applets.
We used to do it because dealing with cross-browser compatibility was a pain. For instance, I used to use a 1-pixel applet instead of XMLHttpRequest for AJAX (slightly before they coined the term "AJAX") and applets for rendering live-updated XML-based diagrams (instead of SVG) in both cases because it simply made things less buggy and less of a pain to support at the time. But that was in 2004 to 2007.
But once we've written something, and it works, we're often a little slow updating it to newer tech, because we can't write a paper out of "the same thing I published earlier, but now using SVG and XHR instead of applets".
If it still just-about works, there's less impetus to rewrite it.