The evaded cadence

In German the term for all cadences that don't resolve to root position tonic is Trugschluss (translated roughly as "deceptive conclusion,") but the way of looking at it is a lot simpler. There's not much importance in what happens after the cadence itself, just what the chord anatomy is. Depending on the musical style that can vary. A tonic in first inversion is considered a Trugschluss in the Vienna-Classic style (Mozart Haydn early Beethoven,) but not so later on where the jumps are much larger. As for functional use, clearly, you'd use something like this if you wanted to extend a segment and still have a recognizable harmony progression.

I think there's not much point in having a special name for this since all it is is a cadence that either resolves and then something happens, or doesn't resolve and then something else happens. But hey, if it helps you put a fancy name on something, more power to you.

As I tend to chromatic harmony I rarely use standard cadences anyway but occasionally resolve onto the mediant or submediant major. With interrupted and imperfect cadences (Va-VIa and I or IV to Va) the question arises about whether you're creating and resolving a tension or suggest you're about to but don't.

I can accept this idea of evading a cadence as a composing tactic though. Approaching the moment and quitting will set up how it's received. If the lead up feels as if a (say) perfect cadence is coming but goes on to an unrelated harmony it could turn into just a surprise.