You need to set up Family Sharing which will allow you to share your Apple Music Family subscription while each member still being able to use their own Apple ID. I am assuming you have simply signed into all the devices with the Apple ID that pays for the family subscription, which would add that persons playlists and data to everyone’s devices.
You can set up Family Sharing by following this help article: https://support.apple.com/en-gb/HT201060
You can find more help with Apple Music and Family Sharing by going to: https://support.apple.com/en-gb/HT205595
However depending on how long iCloud retains data, when you stop paying the individual Apple Music subscriptions, the playlists and data associated with that subscription may have been permanently deleted.