How long ago did her status expire? If it was within the last 90 days, she can apply for Restoration of Status (ROS).
If it's too late for that......
There have been many success stories here from people just like you and your GF. For a sponsorship via an Inland application (SCPLC), the applicant will NOT be refused solely because of a lack of status, because of a Public Policy that is [still] in place. It never guarantees that a person will not be removed from Canada, but the vast majority of those without status are left alone, unless/until the application is refused for other reasons.
Once you are married, submit a SCPLC sponsorship application. Since she is without status, she would not be eligible for an Open Work Permit (OWP) until she receives what is called the AIP (Approval in Principle) email from IRCC. She will be without legal status until she becomes a PR.
However, have the two of you already lived together for at least one full year [anywhere], even while she has been `visiting' you in Canada, which would make you a common law couple?