Word for "parents with children who have moved out"?
An empty-nester is "a person whose children have grown up and no longer live at home". Wiktionary offers the following explanatory etymology:
From birds whose offspring leave the nest when they reach maturity.
When one's children have grown up and moved out of the house permanently, the house is an empty nest, and the parent an empty-nester who may endure empty nest syndrome.
This identity is independent of career, educational, or professional milestones, however. Becoming an empty-nester does not necessarily mean one has more time or is willing to switch to a riskier or less remunerative occupation.