You hit 'refresh'
> Or a broken build throws a script error?
The same thing that happens when a broken build returns a 500---the user can't use that service until the developer fixes it.
Progressive enhancement is a theoretically good idea that---in practice---actually adds a lot of overhead to developers (because every layer of progression is its own UI, with its own user experience and considerations).
_You_ don't, the customer does.
Would you care to name the sites you work on so I can stay away?
Pages I write generally try their best to wrap calls that can fail in a reasonable retry envelope with some intelligent discernment of what response codes can be retried (429, the occasional 420 if someone thought Twitter was cute, the VERY occasional 500 if I just happen to know that the service in question is flaky) and only failing the error back to the user if the client can't retry it. In contrast to the non-JavaScript forms-only sites I've used, which tend to just surface their 429s and 500s straight to the user and expect them to know what a "back" button is (and whether it's safe to resend a form in this context), it's a better user experience.
(Incidentally: I do find myself having to re-invent that "retry envelope with a success handler, fail handler, and filter to determine if the response should be retried" boilerplate over and over as I move among frameworks; if anyone's built a smooth request wrapper for that, it'd be nice-to-have).
This is business, not academia, right and wrong are judged by profit and loss and opportunity cost, not by what is ideal given unlimited resources. Work on feature X or double my work so a few people a day who break their browsers can still use the site... one is practical, the other is not.
In this day and age, most businesses don't care about this type of user. I have no sympathy for those who intentionally cripple the web and don't care to cater to them. You aren't worth it; progressive enhancement isn't worth the effort. It's cheaper to presume Javascript and ignore users like you altogether; don't forget this is business, our motives are profit, not doing things "right".