I can image what happens if tourist board his/her flight time one hour before his I-94 expired. when he refuse scan and grope, TSA might call police and police might detain and arrest him ( though it does not have legal ground, but you never know it could happen). After legal proceeding( guilty, not guilty, imprisonment ), he will be transferred to CBP for deportation proceeding because of expired immigration status.He might end up in immigration detention during the proceeding. of course, he can hire lawyer to speed up processing. TSA might call immigration because of noticing he does not have visa on your passport ( even he does not need one ). Then immigration will take over to begin the deportation proceeding mentioned above. or tsa does not call police or immigration and just refuse him to enter boarding area, he can just surrender himself to immigration and begin deportation proceeding. I do not think deportation proceeding will finish one day unless you volunteering departure in this case no possible. maybe, cpb grant him extension of stay and let him to deal tsa himself.