Hey there, karoliina128! Thanks for reaching out.
It sounds like you have some questions about how your Apple Music subscription works, what's included, and how you can access your music. We can definitely help.
Unlike the iTunes Store, where you can purchase and own digital copies of songs and albums, an Apple Music subscription is a streaming service that allows you to access the entire Apple Music catalog as long as your subscription is active. Additionally, with an active subscription you can download songs for offline play for instances where you might not want to use cellular data, or when Wi-Fi is unavailable.
So, if you let your Apple Music subscription lapse, or if your device is unable to confirm you're enrolled (due to signing out of your Apple ID, or extended periods of time without internet connection) your offline content will be removed automatically. Also, if you run low on space on your device, your offline music can also be removed.
Hope that helps!