When a song gets removed from the Apple Music library, does it stay as a download?

1. You cannot download songs to the cloud. You upload items to the cloud, and songs can be uploaded from a computer to the iCloud Music Library to access from other devices. Songs are uploaded to the iCloud Music Library when they cannot be matched to a track in the Apple Music subscription service catalog.
2. You download songs to a device or computer and can play them while you are subscribed to the service. If the song is removed by the artists from the Apple Music service, it will not longer play on your devices.
3. Songs that are matched to one on the Apple Music subscription service catalog from a computer, will remain there while the song is available. If the matched track is removed from the catalog, it will show a "no longer available" message in the Music App on all devices except the source computer which will retain your original track, unless you delete it yourself.

click here ➜ If songs are missing from your music library after you turn on Sync Library - Apple Support