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Thanks for the fast reply! This clear things up. The first reply sounded a bit evasive to me. I'm new to Android and thought a program that I can't quit would still use resources (as on a laptop). Anyway, I think some other players actually stop running (they're not listed in 'running applications' anymore) when I exit. But some don't, as I know now, so Xiia isn't such a big exception, I guess. Thanks for the explanation!
Every other streaming app I tried has an exit button. I'm uninstalling Xiia because of this annoying shortcoming.