Hi,
As far as I know,Handover failure occurs when UE is trying to do rach to the target cell but failed may be because of sync failure or exceeded preambleTransMax,In which case UE sends reestablishment to the target cell with HO-failure cause.
Path switch request(in case of X2-hanover) and Handover notify (in case of S1AP handover) will go to MME only when target ENB receives the reconfiguration complete message from UE and to send reconfiguration complete message UE will do contention free RACH.
So, Unless UE sends Reconfiguration complete to target cell there is no point to mention about the UE movement to the MME.