Supersymmetry non-breaking $iff$ no "Goldstone fermion"?

In Supersymmetry and Morse Theory (1982) by E Witten,

Concern whether the supersymmetry is broken by checking whether
$$
Q | 0 rangle=0
$$
exists or not — Witten said:

SUSY breaking: A solution may be shown not to exist by calculating a reliable, positive lower bound to the energy eigenvalues.

SUSY non-breaking: It may be shown that a solution does exist by showing that the theory has a mass gap so that there is no potential "Goldstone fermion".

my question is that why SUSY non-breaking has something to do with

• no potential "Goldstone fermion"?
• theory has a mass gap?

Are these if and only if conditions?

$$
text{Supersymmetry non-breaking} iff text{mass gap and no “Goldstone fermion”?}
$$