Generally we do it this way: if it's something simple that doesn't involve the physician doing much, then the original doc gets paid and the doc getting signout doesn't even have his/her name on the chart. The doc writes it up as if whatever is pending is negative and writes the prescriptions as necessary. Something like if a troponin is negative, patient goes home. If the CT abdomen is negative, goes home. The doc leaving usually tells the patient the plan ahead of time. If the patient requires a drastic change in outpatient management or if they require the doc receiving signout to consult another physician, admit the patient, etc., then the doc receiving signout will take over the patient.
Even with that, it's rare to sign out patients. Usually we sign them out if there is a delay. A signout might be a patient pending CT for a kidney stone who is now pain free, or a repeat troponin in a low-risk chest pain patient.