If a positive gate pulse is given to a forward biased thyristor, it gets turned on. What will happen when a negative gate pulse is given to a reverse biased thyristor ?
Nothing... Well unless it is really really high and you get GTO like behaviour ( although the magnitude and di/dt needed to force the abnormal affect is very unlikely)
In normal operation of a Thyristor or SCR, nothing.
Excess voltages of dV/dt spike will eventually cause some kind of transient or permanent breakdown. Excess is a relative term and such operation is usually not desirable.
Triacs have conduction modes in the other quadrants.
Also see this similar question.