This exact situation happened with me prior to starting my current position. Let me tell a short story.
I received a formal offer from the new organization, gave my notice at the previous employer and closed out my projects, and made plans to spend a couple of weeks having a proper several-years-delayed honeymoon with my wife, and then a week visiting family and getting my head ready for the new role. As I was waiting to board the plane to visit my family, I saw on the news that the organization I was joining (government-funded) got a surprise during a weekend political negotiating session, and had their budget for the remainder of the year slashed by a ridiculous amount. This hit them hard enough that they were already talking about furloughs and layoffs to the media, and had an all-hands meeting about the issue scheduled.
By the time the plane landed, I had voicemail waiting for me from the fellow who was going to be my new boss; as soon as he heard what was happening, he immediately started asking his superiors about outstanding offers, and was informed in no uncertain terms that already-issued offers were being honored (but obviously, no new offers would be issued), and he made sure I understood that he was available for any questions I might have. I, along with everyone else in the organization, experienced rolling furloughs for the next few quarters, and a round of voluntary layoffs and additional emergency funding finally helped them make it through until the next budget cycle.
That is precisely how you handle a situation like this: you honor your obligations, and preferably do so proactively, and with a keen eye to how you are impacting people who have placed their trust in you and your organization.
Reneging on your obligations, especially in a situation as nuanced as the posters' (a suggestion to simply "move on" is much easier said than done when you're on an H1B), is the definition of unprofessionalism, and is a direct reflection on them as businesspeople. While I don't recommend he "out" them because of how it might reflect on him later in his career, I'd be lying if I said there wasn't a little voice of schadenfreude in the back of my mind hoping he lets their name slip.