The concept of Hawking radiation is primarily associated with black holes, where it is theorized that particles can be emitted due to quantum effects near the event horizon. The existence of Hawking radiation from all forms of gravitation is not a widely accepted scientific consensus.
However, for the sake of discussion, let's consider the scenario you described: a body in free fall through a cloud of dark matter. Dark matter is a hypothetical form of matter that does not interact with light or electromagnetic radiation, but its presence is inferred from its gravitational effects on visible matter. Since dark matter is not expected to interact strongly with other particles, it is unlikely to generate Hawking radiation.
In the absence of Hawking radiation, a body in free fall through a cloud of dark matter would not attribute any loss of mass to that interaction. The mass loss, if any, would likely be negligible or attributed to other factors.
It's important to note that the scenario you presented involves hypothetical elements, such as the existence of Hawking radiation from all gravitation and the interaction of dark matter with a falling body. These are topics of ongoing scientific research, and any definitive conclusions would require substantial empirical evidence and theoretical consensus.