I know electrolyte capacitor explode when used in AC current but Can we using two parallel electrolyte capacitors as shown in fig. for AC applications since they have lower size than PPC capacitors (for 400v), for using in transformerless power supply as Xc or for power factor correction?
The circuit you show is like a 'roach motel'- charge can get into the caps but cannot get out (as it is blocked by the diodes). So the caps will only provide significant current for the first full cycle.
If you put the caps in series 'back to back' with diodes across each to prevent reverse bias you will get something like a nonpolar capacitor, however many electrolytic caps will not last long with the resulting amount of ripple current- check the specifications carefully.
Without a lot of information in your question, I'm going to assume your transformer less power supply will be converting AC to DC using the diodes. With that in mind, you would use the capacitors on the output of the diodes, across the pulsing DC output for the purpose of filtering the AC ripple. you need to observe polarity in order to prevent the caps from exploding.