Gravestone replacing

[davidft]

just because you are a descendant of someone buried in the grave doesn't automatically mean you have any rights over it.

Where graves were brought outright and where there have been no provisions in wills to the contrary then the "ownership" passes to the senior heir and down their line via senior heirs. The senior heir is the oldest male descendant of the person who brought the grave or failing or failing no0 male heirs then the oldest female etc. If there are no direct descendants it then passes to the next in line in accordance with the rules of kinship

[Dominus]

It could be said that it just goes to show that one needs to keep receipts...
I personally have a number of original receipts for plots in cemeteries and can use them to assert ownership.

If the controlling body for the cemetery is approached, who knows how they may react? They might be overjoyed at the idea of a descendent being willing to do some maintenance - you won't know until you ask...

[stanmapstone]

It will depend on the date. In municipal cemeteries there are Purchased Graves where the applicant purchases the Exclusive Right of Burial in this grave, effectively forming a private grave and giving the family of the deceased control of any future burials in that grave. The owner of the Right must give written permission before any burial can take place in a purchased grave. The Exclusive Right has a fixed term - usually 100 years after which time control of the grave is returned to the relevant authority.

Stan

[Dominus]

That would seem to reinforce the idea of keeping documents.  Admittedly we are in different jurisdictions (I'm in New Zealand and you appear to be in the UK stanmapstone?), but the receipts I hold differ according to the cemetery.
One, referring to the Borough of Devonport's Public Cemetery, implies an extra fee needed to be paid for 'in perpetuity', and the other documents, all for Waikumete Cemetery all identify that right of burial was in perpetuity.

I would guess it all boils down to being careful to check whatever documents the family possesses as well as what official records the cemetery itself has.  Waikumete has detailed records and as such accepted that my family continued to have the right to bury in the plots as late as the mid 1990s without us having to present any documents.