This answer to Is there an upper limit for the internal size of space stations? has this paragraph:
Finally, if you are stuck ["stranded" in the middle of a room in a space station filled with air], you are no longer affected by any decay in the space station orbit. The ISS changes speed, and thus altitude, because of the slight amount of air friction, and must be periodically boosted back up. Eventually the space station will come to meet you. The time scale for rescue would depend on the state of the earth's atmosphere and the shape and orientation of the station.
It got me wondering which way the space station would move relative to the floating astronaut inside it as direct effect of the drag, without anything getting "boosted back up".
It seems to me that the space station will in fact accelerate mainly forwards and slightly downwards at the same time, as it goes into a lower, faster orbit. But the cause is air drag which is a force acting backwards, and because of F = ma that means an acceleration backwards at least initially (I think). But for how long? An infinitesimal time? It seems to me that what makes it hard to think about is the continuous action of the drag.
My question is: What is the acceleration in an orbit decaying due to air resistance relative to one not decaying?