Usually, centrifugal compressor has suction override pressure controller which will open the antisurge valve to protect compressor going to surge due to excessive low suction pressure.
top of that suction override pressure control there is low low suction pressure trip as highlighted above by Root.
Usually suction ESD/UZV valve do not close due to malfuction as they are high reliable valve connected with IPS system. however, we do not negate the scenario. even if scenario occurs, the expectation is compressor suction override pressure controller should save the compressor from tripping itself by opening antisurge control valve. however, it requires very aggressive tuning of controller which is not good during normal operation.
This is best studied in dynamic simulation scenario. In our on going project we have few high pressure (and high sour as well) injection compressors and we have carried out dynamic simulations where-in one of the scenario is sudden discharge block and sudden suction block. We found in some cases compressor was tripping on Low-Low suction pressure. Later, process control has modified the controller tuning and got it saved from tripping when this scenario is occur.
Actually more than suction valve block, the practical scenario is upstream unit tripping.
Hope this helps.