I've basically ignored this "rule" for years because I've never been able to replicate it myself. I test with a handful of screen readers, and none of them have ever cut alternative text short, but I still see the old "125 character limit" knocking about. It's nice to know that someone has taken the time to properly test this, and has firmly debunked it. Maybe, at some point, alt text had a limit; maybe it's just a misunderstanding about how JAWS splits large text chunks up. Either way, a better rule of thumb is: keep alt text concise, but don't worry about length so long as what you're writing is meaningful 😉
No screen reader cut off text altogether. JAWS – and I have tested this with a more recent version of it as well – will split up the alternative text into multiple graphics with shorter alternative text.