“The case-fatality rate is the proportion of persons with a particular condition (cases) who die from that condition. It is a measure of the severity of the condition.”
The formula is: “Number of cause-specific deaths among the incident cases - divided by - Total number of incident cases.”
In other words, “recovered cases” is an extraneous subset of the “total number of incident cases.”
Still hoping this helps...
https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section3.html
In a historical context. Past tense. All cases are resolved. Read more carefully. The denominator is always a closed interval. The numerator can be open, but the diagnosis still has to be within that closed interval.
It’s simple. Stop being obtuse.