Although you may have resolved a criminal matter many years ago, this does not mean that it will not come back to bite you down the road when it comes to immigration enforcement (unless you are a U.S. citizen of course).
I have clients that have criminal convictions from decades ago that come to learn that immigration is only now enforcing such immigration consequences of criminal convictions. As a result, these clients are being placed in removal (deportation) proceedings (immigration court). Can you imagine that the government is now trying to remove these good people (who simply made a mistake) from the U.S. We are not talking about hard core criminals. We are talking about a good citizen who a brush or two with the law.
The discovery of the criminal conviction usually occurs during a trip outside the U.S. and then the reentry into the U.S. , during the process of a naturalization application or renewal of a green card since both require biometrics (fingerprints) to be processed.
The best option for individuals who are currently dealing with a criminal case is to have an immigration attorney work hand in hand with the criminal attorney. If you previously went through criminal proceedings, then before you file any additional paperwork with immigration (whether naturalization or renewal of a green card), consult an attorney regardless of how minimal you think the criminal conviction is. All too often clients seem to think immigration law draws a clear distinction between felonies and misdemeanors. This is just not true. If you value living in the U.S., then make the right decision and investment and consult an attorney before you go any further.