A pose is a position that your body takes at a given time. For example, you pose for a photograph. Ballet dancers pose in particular positions when dancing - they are still at certain points of time. The bird, when it does, has its wings and feet in specific positions. These are not moved post death in order to preserve them. In which... you pose 'in' a postion, so 'in which' refers back to that pose.

“Pose” means bodily posture. We often use the following sentence structure: subject + is/was + in a + (certain pose). So, when the swallows died, their bodies were in a certain pose. “The pose in which they perished” means “the pose they were in at the time of perishing”