What is the apparent weight by a person in an elevator when it is accelerating upwards and downwards?

So I've been learning about the apparent weight of a person in an elevator accelerating upwards or downwards. I learnt that:

If it accelerates upwards with an acceleration a, Apparent weight = m (g+a)

If it accelerates downwards with an acceleration a, Apparent weight = m (g-a)

If it accelerates downwards with an acceleration g, Apparent weight = 0 , i.e, the person undergoes freefall.

I then asked my teacher what would happen if the elevator accelerated downwards with a>g. She told me that normal force would be negative, and would pull the person down.

However, I thought that normal force exerted by a floor can only act upwards, and so a negative normal force can't exist, and thus the normal force would be equal to 0 N.

Could someone please clarify as to what happens in this scenario?