Immigration marriage fraud can take several forms. The would-be immigrant might pay a U.S. citizen to marry or offer to perform a favor in exchange for marrying. Or, there are "mail-order" marriages, where the couple have no preexisting relationship and either or both know the marriage is a fraud. Sometimes an immigrant defrauds a U.S. citizen who believes the marriage is legitimate, while the immigrant knows it is not.
The law pretty much speaks for itself on what can happen to immigrants who commit marriage fraud. The relevant federal law (Immigration and Nationality Act § 275(c); 8 U.S. Code § 1325(c)) states that perpetrators can face prison, a fine, or both, as follows:
Any individual who knowingly enters into a marriage for the purpose of evading any provision of the immigration laws shall be imprisoned for not more than 5 years, or fined not more than $250,000, or both.
People charged with marriage fraud can also be federally charged with visa fraud, harboring an alien, conspiracy, or making false statements. Each such charge carries additional prison sentences and financial penalties.
The extent to which these penalties will actually be applied depends on the specifics of each couple's case. The U.S. government tends to reserve the highest penalties for U.S. citizens or residents who are engaged in major conspiracy operations, such as systematically arranging fraudulent marriages for a profit. For example, in a major law enforcement action in 2019, close to 100 people were charged.
But that doesn't mean that small-time participants in marriage fraud can count on a soft punishment. Ferreting out sham marriages is a top enforcement priority of the U.S. Department of Homeland Security (DHS). Even if the immigrants themselves are not prosecuted criminally, they will in all likelihood simply be deported (removed) from the U.S. and never allowed to return—not even if they later enter into a real marriage with a U.S. citizen.