Most US states stop taxing you once you've genuinely moved away. A handful, commonly called 'sticky states' -- California, New Mexico, New York, South Carolina, and Virginia are the ones most often named -- define residency in a way that makes it unusually hard to prove you've actually left, and some of them start their own tax calculation from federal gross income before the Foreign Earned Income Exclusion is even applied. That means a return that owes the IRS nothing can still owe a sticky state real money on the same income.
Why domicile doesn't reset itself
The core issue is that domicile is treated as 'sticky' in tax law: once established, it continues until you affirmatively establish a new one elsewhere. Moving to India does not, by itself, change a US domicile -- several of these states will keep treating you as a resident owing tax on worldwide income until you can show you've established domicile somewhere else, ideally a no-income-tax state, before leaving the country.
California and New York both offer safe-harbor provisions for people working abroad under a genuine employment contract (roughly 546 days for California, 548 for New York), but both come with strict day-count and, if married, spousal residency conditions. Missing a technical requirement can mean losing the safe harbor entirely, not just partially.
What actually breaks the tie
The most reliable approach cited by cross-border preparers is establishing domicile in a no-income-tax state (Texas, Florida, Nevada, Wyoming, and South Dakota are commonly used) before the move abroad, closing out home ties, driver's licenses, and voter registration in the old state, and keeping careful records of the date domicile changed. This is a state-specific, facts-and-circumstances question -- it's worth a state tax specialist's review before assuming a move to India alone was enough.