When does NDSolve issue zero step size error NDSolve::ndsz?


I want to detect directly when step size becomes "effectively" zero. The below example from the documentation throws the error message as expected:

s = {}; NDSolve[{(2 - f[x]) f'[x] == f[x], f[0] == 1}, f, {x, 0, 5}, StepMonitor :> AppendTo[s, x]];  NDSolve::ndsz: At x == 0.3862940268757776`, step size is effectively zero; singularity or stiff system suspected. 

The below code indicates that none of the actual steps taken has zero length.

AnyTrue[Differences@s, PossibleZeroQ]  (* False *) 

How does NDSolve decide that the step size is zero? I can of course capture the NDSolveValue::ndsz error, but I want to know when exactly (depending on what parameters) the error is issued. In some extreme cases, NDSolve may generate an InterpolatingFunction solution that has practically zero domain length (but not according to PossibleZeroQ).