Negative beta forced in saturation region of BJT?
And what would be the use of having a negative beta ?

To make beta negative either Ib or Ie has to reverse direction.

But when you make Vce &lt; 0 you're using the transistor in reverse mode, the emitter becomes the collector and vice versa. Remember that a BJT has a NPN (or PNP) structure so it can work both ways. Due to doping concentration differences one mode will give a higher beta than the other way. Then beta would still be positive.

So no, beta will never be negative.