A floor can be nowhere near collapse and still be a real design failure. Strength and stiffness are checked against completely different loads, for completely different reasons.
Ask a structural engineer whether a floor is "safe" and the honest answer is: safe from what? A beam sized with plenty of strength to resist its absolute worst-case, amplified loading can still be the wrong beam for the job if it sags visibly, bounces underfoot, or cracks the drywall below it every time someone walks across the room. That's because a structure has to clear two independent hurdles, not one — Ultimate Limit State (ULS), which asks "will it collapse?", and Serviceability Limit State (SLS), which asks "does it stay usable and comfortable under everyday conditions?" Passing one says nothing about the other.