There are states which are entangled, but no pure entangled states can be obtained from them by means of local operations and classical communication (LOCC). Such states are called bound entangled states (BEs).
For bipartite states it means that they are entangled but have zero distillable entanglement. Such states have always nonzero entanglement cost. Bipartite bound entangled states can not be used for teleportation and dense coding directly. However they may help in such tasks if taken as additional resource (activation of bound entanglement). They can also be used for drawing private key.
PPT states if entangled are always bound entangled. Existence of PPT bound entangled states is connected with positive nondecomposable maps. Existence of NPT bound entangled states is an open problem.