There are a number of “only ifs” that precede a PC being responsible for any part of a closed cemetery.
Firstly, it has to have been ‘closed’ by a faculty of the diocese.
Second, there has to have been a request from the PCC to the PC to adopt the closed cemetery.
Third, the PC has to accept responsibility for the closed cemetery.
If any of those have not happened responsibility remains with PCC.
It is very far from being a done deal that a PC has anything to do with a closed cemetery.