I graduated an idol and hired her as staff (she appeared as a stylist). She still shows up in the Formation screen. Is this a bug, or a feature? It does kinda make sense that you could pull her in as she's in the building after all. This was even the plot of an iDOLM@STER episode.
From the patch notes:
"The "idols" section now features a tab for graduated idols (in addition to the default tab, which shows active idols). Here, you can get a glimpse of how idols' lives have turned out after graduating."
The idol does not show on this tab.