Very important stuff, and thankfully Cornell has a pretty well laid out resource, as well as a very helpful & responsive department for this.
https://international.globallearning.cornell.edu/maintaining-your-status
[relevant screenshot]
https://international.globallearning.cornell.edu/travel
International Services at the Office of Global Learning cover a lot of immigration related affairs.
https://international.globallearning.cornell.edu/
You can also get advice from their expert staff by appointment (in-person or Zoom), Email and Phone. You have to schedule appointments in advance (1-2 weeks usually). For emails, from my experience, they respond really fast if your situation is urgent. For phone, sometimes they don't pick up immediately, but I have had an experience when I dropped a voicemail explaining my urgent situation and they called me back fast.