In cases where a student has an unsuccessful semester, the Faculty Committee on Examinations and Standing may require an academic withdrawal. If these are your circumstances, your dean will be in touch with you to explain next steps. An academic required withdrawal is not meant to be punitive; instead, it's a recognition that an unsuccessful semester must be repeated in order for the student to make satisfactory progress to degree. Financial aid does cover a semester repeated for academic reasons. All grades earned in an unsuccessful semester will remain on the transcript; failed courses may be repeated for credit. Detailed policies related to required withdrawal for academic reasons can be found in the Undergraduate Announcement.
Information for students who need to leave the University for a fixed period of time for disciplinary reasons (suspension and suspension with conditions) can be found in Rights, Rules, Responsibilities. A letter about your suspension penalty is sent from the Office of the Dean of Undergraduate Students. Students who have been suspended often have many questions about how this separation will impact their standing. Note that students who leave Princeton for disciplinary reasons will not be eligible to receive University grant aid if they must repeat a term as a result. Depending on the time in the semester that a student is suspended, the transcript may show no courses for the term, Ws, or grades; this is determined by ODUS policies in accordance with the academic calendar. Take a look at the FAQs on this website, and please don't hesitate to talk with your dean, director of studies, or director of student life about your questions and concerns.
The process of checking out and being reinstated is the same for all students, including those with required academic withdrawals or suspensions. Your college dean will be your primary contact for navigating these processes.