We investigate the nature of the idiomatic gapped right dislocation constructions (RDCs), by examining the distinction between the idiomatic and non-idiomatic appendices. The overt idiomatic correlate in the antecedent clause plays a crucial role in identifying the idiomatic appendix of the gapped RDC. That is, the idiomatic appendix in the gapped RDC must hold the idiomatic correlate in the antecedent context. When the idiomatic appendix in the gapped RDC crosses islands such as a relative clause or an adjunct clause, the gapped RDC cannot preserve its idiomatic interpretation even when the verbal idiomatic expression is given in the antecedent clause or question. This is different from the fact that there is a parallelism between the plain gapped RDCs and the fragment answers, which shows a natural consequence under the standard assumption that the appendices and fragments are derived by ellipsis and are island-insensitive due to the repair effect. Hence, we follow the right dislocation approach for the idiomatic appendices in the gapped RDCs, which resolves the issue of the island sensitivity.