Summary: Let \(\kappa^\prime(G)\) denote the edge connectivity of a graph \(G\). For any disjoint subsets \(X,Y \subseteq E(G)\) with \(|Y|\le \kappa^\prime(G)-1\), a necessary and sufficient condition for \(G-Y\) to be a contractible configuration for \(G\) containing a spanning closed trail is obtained. We also characterize the structure of a graph \(G\) that has a spanning closed trail containing \(X\) and avoiding \(Y\) when \(|X|+|Y|\le \kappa^\prime(G)\). These results are applied to show that if \(G\) is \((s,t)\)-supereulerian (that is, for any disjoint subsets \(X, Y \subseteq E(G)\) with \(|X| \le s\) and \(|Y| \le t\), \(G\) has a spanning closed trail that contains \(X\) and avoids \(Y)\) with \(\kappa^\prime(G)=\delta(G)\ge 3\), then for any permutation \(\alpha\) on the vertex set \(V(G)\), the permutation graph \(\alpha(G)\) is \((s,t)\)-supereulerian if and only if \(s+t\le \kappa'(G)\).