Will the job offer be rescided

Hello! I have currently been offered a position that I accepted at a company where security clearance is required. Is it possible that they would rescind the offer when they find that I did not relinquish my former citizenship properly? Or will I be given the choice to relinquish my former citizenship?
I am just worried that I would be rejected due to this. I do not mind properly going through the procedure to relinquish my former citizenship however I am not sure if I should do it on my own now or wait until I hear back? If I do it on my own the embassy requires a paper or statement from my employer as to why I am relinquishing my citizenship…
Thank you in advance for your help!

Perhaps you should clarify, which will actually help you answer your own question: Are you a U.S. citizen with dual citizenship of ____ country? You will obviously disclose this information and depending on the circumstances, may prevent you from getting an interim which in turn may result in a job withdrawal.

The true question is: Are you a U.S. Citizens? (including natural born, foreign born, naturalized) … it’s the requirement to obtain security clearance. If the answer is a no, they actually will rescind the job offer because it should have been specified in the job description if the position requires security clearance.

If the answer is a yes, then:
I think your situation is quite bit same as mine, but it might be different depending on what country you was original from (or original citizenship) and what choice you made. You can see the definition of Dual Nationality on Department of State stating Section 101(a)(22) of the Immigration and Nationality Act (INA).

I specified on my SF86:
I never claimed or considered myself to be dual-national on and after the date of naturalization to be citizens of United States, and I owe permanent allegiance to the United States. I am willing to relinquish and renounce any former nationality and citizenship if required by U.S. law and applicable law of the former foreign nation. I retain the evidence of destroyed/invalidated foreign passport, I am willing to turn in such evidence if required by U.S. law or U.S. law enforcement agency. I have not used foreign passport for any domestic or international travel on and after the date of U.S. Citizenship Naturalization.

The investigator did ask me twice to stating that I’m willing to renounce my former citizenship officially if require by U.S. government. I showed the evidence of destroyed passport (hole-punched and cut the bar code). She did ask me why I keep these invalid foreign passport, and I said it shows all the evidences of my international travel while I was U.S. Permanent Resident and before I become Naturalized U.S. Citizens. I did indeed note that I always present my at U.S. Permanent Resident Card at Port of Entry.

I believe I saw on some forum (don’t quote me on it), but Government of India actually requires you the relinquish your citizenship when you own allegiance to a new country, i.e. obtain a new citizenship.