You can posptone (reschedule) your PMP exam provided your exam is at least 35 days away. You have to email firstname.lastname@example.org in order to do so. The rescheduling is done for free.
If you don't show up to the exam on your exam date, you are considered a "no show" and you will just forfeit your examination fee (there will be no "black mark" on you as an individual and you can still take any PMI exam in the future). However, PMI is considerate when it comes to extraordinary situations such as a medical urgency, so if you don't show up but have a valid reason why, PMI might reschedule another test for you for free. In this case, you have to contact PMI customer care within 72 hours after your scheduled test (the scheduled test that you missed).