  It is shown that the outcomes of measurements on systems in separable mixed
states can be partitioned, via subsequent measurements on a disentangled
extraneous system, into subensembles that display the statistics of entangled
states. This motivates the introduction of the concept of "counterfactual"
entanglement, which can be associated with all separable mixed states including
those that are factorable. This type of entanglement gives rise to a new kind
of postselection-induced Bell inequality violation. The significance of
counterfactual entanglement, and its physical implications, are assessed.
