For now we have a few editable statuses for Vividus Xray Exporter:
xray-exporter.editable-statuses=Reopened, In Progress
For the future:
Please add a possibility for Vividus Xray Exporter to reopen test-cases in "Completed" status, update them and put again in "Completed" status in Jira automatically with Vividus Xray Exporter.