There is no rule about in which octave should the melody or harmony progress or shift throughout the song, let alone rest at the end. It's common though to end with a lower pitch root note as lower frequencies give a more surround feeling than their upper octave counterparts, however the decision to use one or another is highly subjective.
Theory dictates that
Gmaj will resolve at
Cmaj, but it doesn't say that has to be a lower
Cmaj. The functions of these chord progressions are maintained independently of their position over octaves.
An example of building tension when going down is
Am is acting as tonic on minor key.
An alternative to shifting an entire chord up or down over an octave is the use of inversions, which might produce a similar effect without actually moving all the chord notes.
C, no matter the octave, this is called octave equivalency and it's derived from the base that all notes that are one octave apart are musically equivalent. If from
B you add 1 half step or rest 11 half steps, you will reach
C and in either way the tension will release. The only difference is that it will be higher or lower in pitch, but regarding tension both will work in the same manner.
This is why you can play 5 different notes in different octaves (like
C3, C4, E4, G4, E5) and the chord is still called
C, because the musically different notes accross octaves are still
C E G.