When does Kud Wafter fit into the story?
In the paradox world, Kyousuke chooses the "best candidates" not by their cutness (but they  are ^_^) but their life before die.

If you would realize, every non-core member from little busters had a bad life.
In this case, Kud had the feeling to say goodbye to her mother (she didn't it when she was alive).

This spinoff is after the events of Refrain (carcrash + good end = jumper).