Many works deal with the subsequence matching problem using automata structures. It is to decide, given two sequences $s$ and $t$, whether $s$ is a subsequence of $t$. Automata like the Directed Acyclic Subsequence Graph (DASG) or the Subsequence Automaton (SA) accept all subsequences of a set of texts. We focus on this last structure and provide some useful results upon dynamically updates of the SA. Indeed, sequences are indexed as soon as they are processed, allowing to dynamically add or to remove sequences from the set of indexed texts. Moreover, the highlight of these properties also makes it possible to update this automaton whenever a sequence of the set is modified.