Can an H-1B or green-card holder contribute to and keep an HSA, and what happens if they leave the US?

Yes. HSA eligibility depends on your health plan and tax status, not citizenship, so a visa or green-card holder covered by a qualifying HDHP and treated as a U.S. tax resident can contribute and enjoy the same triple-tax benefits. It's one of the most efficient accounts available while you're here.

If you later leave the U.S., the HSA doesn't disappear, but the tax treatment gets tricky. The account stays yours and can keep growing; qualified U.S. medical withdrawals remain tax-free under U.S. rules. However, your new country may not recognize the account and could tax the growth, and non-medical withdrawals face U.S. tax plus a penalty before 65. Get cross-border tax advice before you move to plan the drawdown.