Sometimes, when engaged in conversation, English-speakers will say the first half of a well-known saying or idiom, trailing off at the end or punctuating it with a shrug. For instance, they might say "Birds of a feather..." or "When in Rome..." and leaving the "flock together" and "do as the Romans do" completely unsaid, when arguably that unspoken portion was the whole point of their statement in the first place.
Is there a name for such abbreviated usage?