So what you initially meant was: if the environment changes then those species that are able to adapt to the change survive, and those that can't go extinct. So the dragonfly has been adapting to change for nearly 300 million years while remaining in the same form and habitat, whereas over the same time period reptiles evolved into dinosaurs, pterosaurs, plesiosaurs, mosasaurs, ichthyosaurs, birds and mammals
I think one of your misunderstandings is that, in the context of evolution, there isn't such a thing as
the (singular) environment. Each population has its own environment (apart from anything else, its environment includes the other species in its physical location, in particular what it eats and what eats it). Whether a particular lineage changes depends on a number of factors, including changes in its environment. A population may be at a "local maxima" of adaptation, in other words any changes small enough to be at all probable may reduce its fitness (suitability to its environment). Its environment may change enough to change that situation or not, or it may change too fast anyway, so the population goes extinct. It may change but not in a way that changes the local maxima. So called "living fossils" are comparatively rare, as one would expect, but they in no way contradict evolution.