Administrators can modify the attributes of a review definition at any time, including the Review Owner. If there is a running review instance at the time, that running review instance is not affected by changes to the definition. Identity Governance creates a new version of the definition with the changes and only future runs started since the modified definition will reflect the change.
If you have a review currently running, modifying the review definition does not change the attributes of the current review. The running review always points to the version of the review definition that you used to start the review.
If you assign a new owner to a running review instance, both the previous and new owners can access that specific instance of the review. The previous owner continues to see review runs from before the ownership change and future review runs. The new owner sees only that review run. You can also change the review end date and time for a running review.