** This is not an official answer, I may be wrong.
With OCI/PIO card, you can stay in India as long as you want. There was a rule after every 180 days, you need to register in local Police Station about extension of your stay, however since 2014 (with Modi Govt) they abolished the rule. However I dont have much idea about Tourist visa requirements for overstay.
Me/My wife(Malaysian citizen and Indian PIO card holder) traveled to India in 2013, we did overstay of little over 180 days, while returning back to the US, we were questioned and fined. Luckily we were little early at the airport, that we did not miss our flight for questioning and fine process.
I would suggest check all resources online, if needed apply for OCI/PIO card. OCI/PIO card mostly does not have overstay limitations.
(My answer is based on your daughter being an American citizen with an Indian Visa. That is what I understood from your question, if I am mistaken please correct me.) Hello, over-staying your visa in India, like most countries, is a crime. It is punishable most commonly by a fine and the costs to apply for an extension, but by law they can detain, imprison, and deport you. Now as far as being stopped when leaving the country, it would most likely be to pay the fines associated with over-staying, as you are already leaving the country odds are they wont detain you. Returning back to India will require her to obtain a new visa, or an extension on the current one. I hope that this helped you and good luck. I forgot to add, that depending on what kind of visa she has, she will actually have to leave India and apply for the extension back in the USA. You can try to mail it out through a friend outside of the country, but it is not recommended.
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