A K-1 is a NON-immigrant visa which means the I-94 expires after 90 days. When an I-94 expires, the visa holder is immediately out of status.....and deportable....as is the case with any non-immigrant visa. Marriage to a US citizen confers no right to remain in the US. By DOS policy, a K-1 entrant is granted "authorized stay" ONLY after submission of a proper I-485. "Authorized Stay" is not a legal status, but allows the applicant to remain in the US until the I-485 is either approved or denied. This is a DHS POLICY....not law.
To fulfill the conditions of the K-1, you must marry within 90 days....but that gives NO right to remain in the US. Even after submitting a proper I-485, the applicant is out of status, but not accruing additional unlawful presence. It is strongly advised to submit a proper I-485 before the 90 days after entry have elapsed to avoid accruing any unlawful presence. This is especially important with the current administration.
FYI- Search "spaceage" here on VJ for an example of someone who married after a K-1, yet did NOT file an I-485 within 90 days. That person was apprehended by police and spent weeks in jail.