The question is easy to answer. Yes, this is a development that shows up from time to time. Species displaying only asexual reproduction all tend to be evolutionarily young, which implies that adopting the strategy rapidly leads to extinction, but it has short-term benefits which mean that there's usually something around trying it out. (And then there are species with obligatory parthenogenesis and also obligatory sexual reproduction, like aphids, which don't experience the problems that pure-cloning species do.)
By way of examples of sexually-reproducing species shifting to parthenogenesis, there is a species of lizard that can only reproduce that way. We can be certain they originally reproduced sexually since they still engage in a (pointless) simulation of copulation.