Although introduced for entanglement, quantum repeaters and swapping protocols have been analyzed for other quantum correlations (QC), such as quantum discord. Introduced by Mundarain and Ladrón de Guevara [43], local-available quantum correlations (LAQC) are a type of residual quantum correlation mostly overlooked in the literature. Recently, Bellorin et al. [44, 45] obtained exact analytical results for its measure for general 2-qubit X states. Building on those results, we analyzed the behavior of this measure in a standard quantum correlation swapping (QCS) protocol, focusing on 2-qubit X states as the initial states. As expected, we find that if the initial states are non-classical and the one used for the projective measurement is entangled, the final state will, in general, have non-zero LAQC. Using its properties, we establish the conditions required for the final state in the QCS scheme having a non-null LAQC measure. We illustrate these results by analyzing six relevant families of one-parameter 2-qubit X states. Within those examples, we included mixed states that result in a separable state but a non-zero LAQC measure. We also included a separable quantum-correlated mixed state that remains separable and quantum correlated after the QCS scheme.