I know that above the critical temperature and pressure, at the boundary between the liquid and gas phase disappears. But does this also hold when temperature is below critical temperature but pressure is above critical pressure? Or do we observe a different phenomenon?
If the temperature is below critical temp and the pressure is also below its critical value then there is a possibility that we see an equilibrium between the liquid and gaseous states.
When one of them is above their critical value it is impossible to change the state of the substance from gas to liquid by merely changing the other parameter. For instance if $T > T_c$, then no matter how much you try to increase the pressure, the gas will not liquefy. Similarly if $P > P_c$, you can't have a gas-liquid equilibrium in any temperature. It's clear from the given picture.