The reality is that even if he marries you, a US citizen, this will not cure the fact that he has been here illegally in the US for an extended period of time.
Overstaying the expiration of a valid visa by more than one year, would normally subject someone to a 10 year ban from re-entry into the United States.
Entering the country illegally or through fraudulent means can result in a lifetime ban from the United States.
This is something that even marrying a US citizen cannot fix. However, there is one avenue, which is the 601 waiver which allows person who are subject to a re-entry ban to make a plea to have that ban lifted.
There is no appeals method for a denied 601 waiver, so my recommendation would be to have an attorney assist you so that you can get it submitted correctly the first time. Reasons for requesting the waiver involve showing that he would suffer extreme hardship by not being allowed to be in the US, for example separation from family and/ or children. He should also show any and all ties that he has to the US to help make his petition more persuasive.
Please keep in mind that even though there is this route of applying for the waiver, it is not guaranteed, and too many times there are persons who receive a denial. I truly wish the best of luck to your husband and family though.
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