The deal is--the musical tidbit that you know is wrong--it isn't necessary for a musical phrase to end on the tonic--simple as that. It can end on any note.

The feeling that a melody needs to resolve comes from something a bit different--it comes from movement from tonic to dominant harmony--and you can write melodies without this, too--

When you write a tune using the diatonic scales that we use them in western music,you create tension by moving back and forth between tonic and dominant harmony(between notes that are within the C chord harmony and notes in the G7 chord harmony)-after a certain number of counts, it l leads you to back to the tonic, because that is what our western music tends to do, our ears have learned to expect it. But it doesn't have to be that way. There are major scale melodies in music from other places, in Serbian folk music, for instance, that end on the dominant--

But there is a lot of music that doesn't create tension by moving to the dominant--so you don't feel that need to resolve at all. Indonesian Gamelan music is like that--and, a bit closer to home, pentatonic scales are like that. When you use pentatonic scales to construct a melody you don't ever move to dominant harmony, so you don't need to resolve.


Anyway, when you create melodies without shifting from tonic to dominant harmony, your ear won't tell you that the last note is unresolved, no matter what it is. You can experiment with this
If you pick out a melody, using only the notes in, say, a C 6 chord(C E G A C), and ending on different notes in the chord.