In case of X2 based handover ,where MME doesn't involve in handover preparation, handover allocation etc , PATH SWITCH REQ message is necessary to be sent to MME to modify downlink direction of data.
Once MME receives this PATH SWITCH REQUEST message, based on the eNodeB , it decides that SGW relocation is required or not. If it is required then MME sends Create Session Request message to new SGW with an indication that SGW shall send Modify Bearer Request message to PGW. PGW responses with Modify bearer Response to SGW and then SGW responds back to MME with Create Session Response message.
If SGW is not relocated in X2-based handover, MME just sends Modify Bearer Request message to SGW and SGW responds back to MME with Modify Bearer Response message. Since SGW is not relocated then it's SGW's responsibility to clear the resource resource at source eNodeB. To do so, SGW sends End marker message to source eNodeB and in turn source eNodeB sends to target eNodeB. This way downlink data flow direction gets exchanged in X2-based handover with SGW relocation . Of course, MME will send final message i.e. PATH SWITCH REQUEST ACK message to target eNodeB to finish the procedure.
When SGW gets changed in X2-based handover, target eNodeB instruct to source eNodeB to release the UE context by sending UE Context Release message.