My fiance came on a tourist visa and stopped by immigration, put a dated stamp on her visa to leave, can she still stay?

That would be fraud. Likely, the reason she was stopped she did not have 'non-immigrant intent'. *Fiancee Petition* A Fiance Petition needs to be prepared. This is a petition that will allow your fiance to come to the U.S. in a relatively short period of time. Usually, it takes around 6 to 9 months for the petition to be approved at immigration in the United States. Subsequently, the approval would be sent to the U.S. Consulate or Embassy in your fiance's home country. When your fiance comes to the U.S., you will have ninety days to get married. Our firm can prepare the entire Fiance Petition and make it so it goes smoothly and correctly. You have to have physically seen your Fiance in the last two years.

She should be able to apply for adjustment of status while in the United States. But this could depend upon what USCIS stamped in her passport.

Yes, as long as she entered the US lawfully, she can overstay and get married to a US citizen and then apply for permanent residence on the basis of that marriage. Please let me know if you have any additional questions or how I can be of further assistance to you in this matter.