If the songs are in a format that only that app can play, and the app stops working after the trial unless you pay for it, the files stay there, but you can't play them because you have no working app that plays that file format.
If they're plain mp3 files, or some other unencrypted audio format, you can still play them with some other app, you're just violating copyright.
Since I've never downloaded the trial app, I can't foresee which one is going to happen. I can't even make an educated guess - it's a fair coin toss - but if I were writing the app, I'd make sure that you had to pay to play. (I don't write apps - for any environment - for money any more. If I release something now it's free. If it's for money, I'd be sitting in an office creating the program - which I retired from doing a few years ago.)