Could I marry an illegal immigrant?

Although not completely clear from your question, I presume that you are a U.S. citizen. Generally, if a U.S. citizen marries a boyfriend who entered the U.S. lawfully and with inspection (such as with an F-1 student visa), the couple could petition for him in the Immediate Relative visa category notwithstanding that the boyfriend had overstayed his previous student visa. Of course, that would be possible only if the couple entered into a genuine bona fide marriage, and not a fraudulent one entered for the purpose of getting a "Green Card." A criminal arrest or conviction may, however, stand in the way of eligibility to gain immigration benefits in that way. This is true regardless of whether a conviction becomes expunged. Not only would the foreign national need to honestly answer the question about having ever been arrested or convicted, but the arrest and conviction almost certainly will be revealed in the security background check that is a part of the immigration application process. That, too, is accurate notwithstanding a court-ordered expungement. If a criminal defense attorney tells your boyfriend otherwise, your boyfriend (and that attorney) should speak to an immigration attorney to learn the facts about this. Further, false statements in the immigration process can have profound and harsh consequences, and all applications must be answered accurately. A petty theft conviction may or may not have immigration consequences. Sometimes there are steps that can be taken after a conviction to mitigate or avoid immigration consequences even if the initial conviction would have immigration consequences. An immigration attorney, after learning all of the relevant details and reviewing court-certified copies of the arrest disposition documents, could advise about this. Note that if a criminal conviction becomes expunged, it can be very difficult and expensive to obtain court-certified copies of the relevant documents, and it would be a serious mistake to seek an expungement before consulting with an immigration attorney about the court-certified copies of documents that may be needed. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.