Can a foreign citizen apply for an Indian X Visa?

One thing worth clarifying is that X Visa is an Entry Visa, not a general-purpose alternative to the tourist visa.

The Government of India lists the Entry Visa category separately and says an X-1 Visa may be granted to a Person of Indian Origin who does not possess an OCI card. X-2 is for certain family members of Indian citizens, Persons of Indian Origin and OCI cardholders.

If you previously held an Indian passport, your cancelled passport is particularly relevant because the official definition of Person of Indian Origin includes someone who at any time held an Indian passport.

For someone who has never been an Indian citizen, the relationship-based X-2 route may be the relevant one if they are the spouse or child of a qualifying person.

I would still check the exact current document checklist with the Indian Mission handling your application. The online regular visa system is intended for foreigners applying from outside India, and the application process requires supporting documents and passport submission according to the applicable Mission procedure.

My situation was different because I never held Indian citizenship.

I'm Canadian and married to an Indian citizen. I applied based on my relationship with my Indian spouse rather than claiming Indian origin.

The official visa provisions distinguish between X-1 for a Person of Indian Origin without OCI and X-2 for the spouse or child of an Indian citizen, Person of Indian Origin or OCI cardholder.

So I wouldn't assume that every foreign citizen qualifies for X Visa simply because they want to stay in India for a long time.

Your relationship with India matters. If you previously held an Indian passport, that is a very different situation from someone who has never been an Indian citizen but is married to an Indian national.

I would prepare your old Indian passport, Surrender Certificate and any other proof of Indian origin, then check the current instructions of the Indian Mission where you're applying.

Yes, the X Visa isn't limited to people who currently have Indian citizenship.

I became a U.S. citizen and surrendered my Indian passport but hadn't obtained OCI when I applied for an Entry Visa. My understanding was that I qualified under the Person of Indian Origin category rather than applying as an Indian citizen.

The official Indian visa information specifically lists a Person of Indian Origin who doesn't possess an OCI card as eligible for an X-1 Visa. It also defines a Person of Indian Origin for this purpose to include someone who previously held an Indian passport.

I submitted my current U.S. passport and documents showing my previous Indian citizenship. I also kept my surrendered Indian passport and Surrender Certificate available.

I wouldn't rely only on what another applicant submitted, though. The Mission can ask for supporting documents depending on the individual case.

Also, X-1 and X-2 aren't interchangeable. X-2 is generally for spouses and children of an Indian citizen, Person of Indian Origin or OCI cardholder who aren't themselves OCI cardholders.