I am now using the 3-month free trial of Apple Music. Yesterday, I downloaded a few albums into my iPhone. If I do not join the subscription after the free trial period, will the songs still be in my iPhone?
No - as Apple says here
*You can save music offline on up to 10 devices. These songs are accessible only during your Apple Music membership.
Note that you do not need to 'join the subscription after the free trial period', Apple will just start charging your credit card for the subscription.
The point of offline files is so that you can listen to Apple Music without using up your mobile data usage, not to download music to keep forever.