Is there a term for an $A$-module $M$ such that $M \otimes_A -$ takes nonzero modules to nonzero modules?

Motivation: It is a standard theorem that if $B$ is faithfully flat over $A$, then $\hbox{Spec } B \to \hbox{Spec } A$ is surjective. However, looking at the proof, this only really requires the property above--you need to know that every fiber is nonempty, i.e., that the rings $B \otimes_A \Bbbk (x)$ are nonzero for $x \in \hbox{Spec } A$.