@lomanfeusagach @beeoproblem @caseyliss @gruber

Yes, that's correct. However, this does require the new employer to be willing to sponsor your H1B application. They are the ones who have to file a petition with USCIS to start the process. It is some bother for them but it's certainly doable. Anyone who hires H1B people in the first place would know how to do it. And this step is exempt from the quota requirements unlike the original H1B hiring. however, this all takes time and there are deadlines so as a practical matter you need to line up the new job and start the process in advance, otherwise it's easy to lose status and that's the last thing you need when dealing with US immigration. The grace period after an H1B person is fired or their contract ends is just 60 days. When I switched employers on H1B visa my new employer filed the petition a couple of months before my old contract expired. I am in academia, not industry and universities are familiar with the process so this was fairly straightforward.

H1B visas are only extendable for up to 6 years (I had to leave the country after 6 years on H1B) so by my count of initial applications from the data on https://www.uscis.gov/tools/reports-and-studies/h-1b-employer-data-hub?fy=All&items_per_page=100&naics=All&state=All&topic_id=Twitter twitter has at most 429 ppl on H1B assuming nobody left or was fired and everybody stays for the max allowed time. which is of course not the case. so I expect the actual number is maybe half that.