I completely understand your confusion,
@Orion. Here's how the story goes:
Modern voltmeters have
very high input impedance (in this case, the DC resistance component of that is what's relevant), and present almost no load to the circuit under test (which is ideal). The cell in question has a very high internal resistance (due to unknown failure / degradation). Your voltmeter, as it draws practically no current, will see the difference of potential (voltage) across the output terminals of the cell, so it will read the voltage of the cell despite the excessive internal resistance (effectively open-circuit / no-load conditions).
The sum of the voltage drop(s) across all resistive elements in a circuit will always equal the source voltage. When the circuit is completed, as when a load is placed across it (the light is switched on), all / most of the voltage provided by the cell will be dropped across that (abnormal) internal resistance of the cell. That internal resistance is essentially acting as a large 'current limiting' resistor, so the cell can provide little or no actual current, and is not sufficient for the load (flashlight) to operate on, so it will be appear 'dead'.
When the circuit is completed (a load is placed across the cell), if you were to connect your voltmeter across the cell (or load connection) in parallel, you would measure zero (or very little) voltage, because that voltage is being mostly dropped across the internal resistance. The load can therefore draw little / no current from the cell. The potential difference (voltage) of the cell can be measured when there is no load on it (open circuit), therefore you will measure that across the cell. As soon as the circuit is completed and a load is placed across the cell, most / all of the voltage you measured 'open circuit' is then being dropped across that internal resistance, and thus your voltmeter would measure little / no voltage, the load will not see it, and cannot operate on it. If you could practically connect your meter in this way, that's what you would see. If you instead connected a current meter in series with the circuit, you would likewise measure little / no current.
If the light you're using is 'known-good', and works OK with a known-good cell, the cell you're having problems using is defective and should be disposed of. Do not attempt to 'post mortem' the cell (to try to determine 'root cause'), as that could easily end in tears. Just dispose of the cell safely without further thought on the matter, as previously recommended. Now that you know what's 'wrong with the cell', I would suggest that you not worry further about what
caused it internally. Cells can / will fail, and in this case, it 'failed safe', which is how we hope thay will fail (vs some 'china syndrome' type event