to trave from high to low and back you should be only a short time in the "frobidden" state. Therfore sometimes you see a min dV/dt rise rate or fall rate.
To your question:
Usually the IC will not be damaged. But with some Ic you will see oscillating (depends on source impedance) and usually you will see increased VCC current caused by crow bar currents of th IC´s input stage.
Avoid this for low power (battery powered) applications.
So even if we give a fixed voltage in the forbidden state also,this oscillation will occur?
I mean instead of of a pulse,if i give a fixed 1.5V,will that cause oscillation?
if you give a low impedance voltage to the input it is unlikely to oscillate. But state/function is not predictable.
Maybe a schmitt trigger single gate logic could help.