An empty sequence is a (finite) sequence containing no terms.
Thus an empty sequence is a mapping from $\varnothing$ to $S$, that is, the empty mapping.
Thus by definition an empty sequence is a (finite) sequence whose length is $0$.
An empty sequence is also known as a null sequence.
However, this term is not recommended as it is also in general use to mean a number sequence which converges to a limit of $0$.