Apple Music songs when canceling account and starting a new one If I cancel my Apple Music membership and start a new membership will I be able to play the songs I downloaded from my previous membership? Will they still be in my library?
As long as the two Apple Music subscriptions are tied to the same iCloud account, your music will remain in your iCloud Music Library, and will all be accessible and playable once again after you sign up for a new subscription.

For instance, if you switch from a Family plan to a personal plan, your music should not disappear, so long as you don't delete the music from your iCloud Music Library.