Travel back to India from US for good with no passport

I believe the reason that the Indian consulate requires proof of valid status to issue you a passport, is because they are trying to prevent people who have naturalized in the U.S., and thus have automatically lost Indian citizenship, from still pretending to be Indian citizens. Having proof of valid non-citizen status proves that you currently (or recently) was not a U.S. citizen. If someone has already naturalized, they (usually) have no proof of status in the U.S. other than their proof of citizenship, which would alert them that you may not actually be an Indian citizen.

Unfortunately, this means that people who are out of status, like you, are stuck. (It's kind of a Catch-22 -- you are illegal, but can't leave because you need a passport to do so, which you can't get because you're illegal.) Basically, I think they need you to provide them some proof that you do not have status, or otherwise is not a U.S. citizen. Unfortunately, there isn't really such a document that you can apply for. I would have thought that the Extension receipt or denial would be sufficient (did you try that?), because it shows that you were recently in a nonimmigrant status, and trying to extend it; and someone who is a citizen, or almost a citizen (permanent resident) would not apply for such a thing.

Maybe you should ask the Indian consulate what is an acceptable proof that you are out of status in the U.S. I have heard that in some such cases, people have gone to the Social Security Administration to get a document that you are not listed as a citizen in the Social Security database (even though this is not a good proof, because you're the one who needs to tell Social Security to update your status when your immigration status changes). If you can get that, you can try that.

I guess in the worst case, you can report yourself to the ICE, and get yourself deported, in which case they will tell the Indian consulate that you are illegal, and work with the Indian consulate to get you a travel document. Though this is kind of an extreme case and if you really go through deportation, you will have consequences, e.g. 10-year ban.

Update: Looking at the BLS page on renewal of Indian passport after it expires, it seems to clearly mention an option for people who are out of status in Documents Requirements:

Notarized Color photocopy of current valid US visa on passport or Green card or Employment Authorization Card or I- 797 approval notice documents. Student visa Status holders must enclose I-20 Document as well. If your visa has expired and/or or you have the receipt notice for extension of your visa then: NYC, SFO & HOU Jurisdiction Applicants - must provide a notarized no status affidavit with photocopy of the valid passport and the green card of two witnesses duly notarized + 7 Copies of Nationality Verification Form (Given in Point 2 above) are required and each copy must have an original photograph affixed on it. WAS/ATL/HOU/CHI Jurisdiction Applicants - must visit the consulate in person for an interview before applying at the passport application center.

This seems quite simple. India wants proof of your status in the USA, so get it for them.

Walk into US immigration, explain what's happening, and get a letter from them declaring your status as H1B, about to expire, not being renewed, and that the US Government would appreciate it if you departed the country before a particular date. Signed, stamped, with a name and callback number.

deportation usually means you declined to leave on your own and the government forces the issue. You appear to be trying to leave, your own government is making that difficult and you need some assistance from Uncle Sam.

At http://passport.blsindia-usa.com/sample_form/Affidavit_for_Status_Example_file.pdf (linked from here) there is an example of a declaration meant to be made by out-of-status Indian citizens in the US when applying for passport renewal. It doesn't seem to be directly applicable to you, because it requires a good reason that you have not renewed in time -- but notice the last item:

16. I hereby undertake and agree that if the short validity passport issued to me is lost, I would not be granted further passport facilities and instead one way emergency certificate would be issued to me.

(my emphasis). This indicates that there's such a thing as a one-way emergency travel document that can be issued on more lenient terms than a full passport. You might try to inquire at the consulate specifically about how you can get such a thing, if you don't qualify for overseas issue of an actual passport.

The note at the bottom of this page seems to indicate that you should contact the consulate directly, rather than BLS, about this.