As per the ITIL framework, Incident record used for auditing purpose for tracking production issues. Depending on the impact on services Incident Record can have different priorities and resolution times as per the defined SLAs.
Standard practice says that incident can only be closed when impacted service is restored. Some companies follow the strict practice of tagging every single incident to the PM record for RCA. Ideally, from my view for the one-off incident should be considered as out of scope for problem management. The definition of Problem says an Unknown fault with the service/application which needs root cause analysis followed by the permanent fix. Therefore, to summarize problem records are the mandatory parameter for delivering in-life fixes discovered via incident management route. Except proactive problem management which helps to resolve fault in live service which hasn’t caused service impact.
Coming back to Incident resolution what if we don’t have the workaround. A workaround is set of activities Support team performs as part of the temporary fix to restore service. So, in this case, we cannot close this incident since service is not restored and problem record can only be raised when the incident is service restored leaving catch-22 situation. The solution to this is to leave Incident Open and deliver permanent fix under incident without creating problem record followed by service restoration.