Large parallel computer systems bounding experience faults are inevitable due to their scale sizes, which poses serious reliability challenges for interconnection networks. Two new indicators were recently introduced to assess the stability of these networks more accurately, including structure connectivity and substructure connectivity. These parameters are crucial in measuring fault tolerance during chip failures. Let H be a certain graph pattern, and \(\mathcal {F}\) be a set of subgraphs in a graph G. Then, \(\mathcal {F}\) is called an H-structure cut (resp. H-substructure cut) of G if every element of \(\mathcal {F}\) is isomorphic to H (resp. isomorphic to a connected subgraph of H) when \(G-\mathcal {F}\) is disconnected. The H-structure connectivity \(\kappa (G; H)\) (resp. H-substructure connectivity \(\kappa ^s(G; H)\) ) is the minimum cardinality over all H-structure cuts (resp. H-substructure cuts). Recently, Ba, in her Ph.D. dissertation, posted the result of \(K_{1,r}\) -(sub)structure connectivity of \(FCQ_n\) for \(1\le r\le \frac{n}{2}\) , where \(FCQ_n\) denotes the n-dimensional folded crossed cube, which is a variant of the hypercube called crossed cube by enhancing a folded link between any two complementary vertices. In this paper, to supplement the completeness of the findings of this study, we successfully determine the \(K_{1,r}\) -(sub)structure connectivity of \(FCQ_n\) for \(\frac{n}{2}+1\le r\le n\) , which solves the open problem proposed by Ba.
