Let $S$ be a string over some alphabet $\Sigma$. It is well known that a substring of $S$ is commonly defined as a sequence of contiguous elements from $S$, while a subsequence of $S$ is a sequence made of non necessarily contiguous elements from $S$ (e.g. if $S="123465835"$, then $"4658"$ is a substring of $S$ while $"1236"$ is a subsequence of $S$). But is there a word to refer to subsequences that can be obtained from $S$ by removing an arbitrary substring (e.g. $"12835"$)?

(this concept seems complementary to that of a subsequence, hence the conjectured "co-subsequence" in the title -- although "co-substring" might be a good choice too)