Historical/derivation approach:
This scenario reflects the classic experiments that separated the "light reaction" from the "dark reaction" of photosynthesis. When the thylakoid membranes (site of the light reactions) are removed and only the stroma remains, the stroma still contains the full set of Calvin cycle enzymes, including RuBisCO, needed to fix \( \text{CO}_2 \) into carbohydrate.
What the isolated stroma lacks, once separated from the lamellae, is a supply of chemical energy and reducing power that the thylakoids would normally generate from light. If this energy currency, \(\text{ATP}\), and reducing power, \(\text{NADPH}\), are supplied artificially, the dark reactions can proceed even in complete darkness. This is why light itself is not directly required by the stroma; it only needs the products of the light reaction. Oxygen and carotenoids play no role in driving \( \text{CO}_2 \) fixation in the stroma.
Hence, supplying ATP and NADPH allows isolated stroma to fix \( \text{CO}_2 \).