Recover downloaded songs after trial cancellation

An Apple Music trial is a time-limited free subscription to the Apple Music service. You can only play the music for as long as you have a subscription. The alternative is actually purchase the tracks, in which case you can play your own copy for as long as you have a copy on your devices.

Buy music from the iTunes Store on your iPhone or iPad - Apple Support

Buy or download music from the iTunes Store in Music on Mac - Apple Support

Limnos wrote:

The alternative is actually purchase the tracks, in which case you can play your own copy for as long as you have a copy on your devices.

Buy music from the iTunes Store on your iPhone or iPad - Apple Support

Buy or download music from the iTunes Store in Music on Mac - Apple Support

The OP might also want to see Import songs from CDs into Music on Mac - Apple Support . Macs no longer have optical drives, but there are many people who have large CD collections, and it is not difficult to get external USB optical drives.

CDs are largely gone from brick-and-mortar retailers, but fortunately not from mail/Web-order ones … yet.

Limnos wrote:

Since the OP was referring to "downloaded" songs I presumed these did not originate from CDs. Nor LPs. Nor cassettes. Nor reel-to-reel.

I didn't say that they did.

The OP appears to have downloaded a couple of hundred "offline listening" copies of Apple Music subscription songs, which, of course, were rentals that were "cancelled" when the OP decided to cancel the free trial, rather than paying for a continuing subscription. If the OP wants to access subscription songs again, the OP needs to sign up for a paid subscription.

I was just commenting on the other part: "The alternative is actually purchase the tracks …"

Although the Apple Music subscription service allows you to download "offline listening" copies, these are just for convenience, so that you can listen to music even when not continuously connected to the Internet.

They are still rental songs, and if you stop paying for a subscription, you lose access to them. A "subscription" to some streaming service like Apple Music, Spotify, or Netflix is more like paying for cable TV (stop paying and they cut off the cable feed) than it is like a magazine subscription (where you just stop receiving new issues – but can keep all of the ones you have received).

It's also my understanding that if you let your Apple Music subscription lapse, all of your "offline listening" copies and all of your playlists that contain subscription songs get deleted quickly. If you resubscribe, you may find that you have to re-download "offline listening" copies and re-build playlists all over.

If you no longer subscribe to Apple Music, you will not have access to the downloaded music.

Since the OP was referring to "downloaded" songs I presumed these did not originate from CDs. Nor LPs. Nor cassettes. Nor reel-to-reel. Now my collection does originate from all of those. I just didn't feel I needed to make my reply that expansive. ;-) If you wish, I could outline how to get tracks off all of those but it will take me about 3 posts.