Resignation Letter

When an employee quits, are they obligated to send a formal resignation letter or email? What happens if they do not? Generally if we have an employee quit, we ask for the notice with the end date in writing however sometimes it’s just verbal and they forget to send something in writing before they leave. Our Payroll has an issue with issuing an ROE without the resignation letter so I am just looking for guidance from others on this.I’m sure in many cases, people quit without issuing a formal notice in writing. As a side note our field employee’s are paid out vacation and do not receive any other benefits, so we process their resignation letter and issue ROE accordingly without any other formal communication in writing on our end. However, If we (the company) are initiating a termination, or lay off, than we would issue a formal letter to the employee outlining the reasoning and details of the termination.