You can. Even when the line is completely extinct the people ruling are referred to as regents, until proper royalty is formally established again. Sometimes that could even take decades, if there isn't a clear line of succession and since Anduin never got laid, never named a successor(outside greymane) and has no cousins that's not an option.
If you really want an extreme example Denethor's line from Lord of the Rings did it for generations, because the real King was prophetsised to return.