Boundless can typically help spouses of U.S. citizens who do not currently have a valid immigration status — that is, they have an expired visa — to apply for a marriage-based green card from within the United States. Generally this is true as long as the spouse seeking the green card entered the United States: 1) lawfully (with a valid visa or under the Visa Waiver Program) and 2) "with inspection," meaning they were screened by a Customs and Border Protection (CBP) agent upon arrival.
In this situation, the couple would follow the same application process for a spouse who is married to a U.S. citizen and has current lawful immigration status.
There are, however, some important travel considerations for the undocumented spouse. This detailed guide has more information.
Unfortunately, Boundless cannot help spouses who did not enter the United States lawfully and spouses who do not have current lawful immigration status and are married to U.S. green card holders (lawful permanent residents).