Cancelled subscription, lost the rest of the month, how to get money back or re-subscribe without paying again?

I'm used to cancelling monthly subscriptions after I buy them so I can finish the month without having to worry about getting auto-charged. Usually this works perfectly for every service I've ever used. But for some reason when you cancel your Apple Music subscription it will stop your service immediately rather than letting you finish the month you paid for. I paid for it yesterday and then cancelled today and I pretty much just lost my $10. I tried to re-subscribe and they want another $10.

Is there a way for me to get the month subscription back without having to pay a second time?? I'm pretty shocked that they would do something like this.