If a woman has a Visitor’s Visa but then gets married in US, files I-485, will they process application and let her stay or will they send her home?

Generally, a foreign national who enters the U.S. lawfully and with examination (such as with a visitor's visa), and who later becomes married to a U.S. citizen, may succeed in a marriage-based adjustment of status application without any need to travel abroad for consular processing. This is true even if the foreign national may have overstayed or otherwise violated a nonimmigrant visa. There are exceptions, however, where the USCIS could conclude that the foreign national fraudulently entered the U.S. with a visitor's visa while intending to marry and stay in the U.S. permanently. It would be wise for the couple to consult with an immigration attorney who, after learning all of the relevant facts, could advise about immigration eligibilities, options and strategies and could offer legal representation in the often quite complex application process.