I'm basically about to vomit information at you that may or may not make sense.
Echo is Euca's wish, depending on the route you take, he gets weaker and weaker, whatever we're doing is either straying away from the path to fulfilling our wish, or the opposite and getting closer, so he would just disappear when we complete it. However, it could also be that since he refused to tell us what we wished for, which means he's consciously trying to avoid fulfilling the wish. Side note, when taking Sissel's route, after rewinding time, your will to fix the past is strengthening, so shouldn't Echo get stronger?
Remnant isn't just a wish away, he has ungodly strength, but we never really know why he is there to begin with, we don't even know who brought him into existence. That being said, he wouldn't haunt the main cast in particular if it had nothing to do with it, so is he a wish Euca had made with a full throttle will during a low in his life? Is he the result of a really fucked up Echo, after avoiding his whole purpose, and remained after Halley rewound time, who is he even linked to?
Everyone has a wish guardian in one way shape or form, Remnant isn't directly linked to anyone, all he's shown the desire for is utter chaos, or.. or the truth, he's also shown minute kindness in giving someone what they want, even if it isn't always the best thing for the person