Even if your ancestor's name is not on the plaque, it doesn't necessarily meant s/he was not buried there. The memorial stone is not comprehensive - the inscriptions reflect only the names that could be found, not everyone ever interred in the cemetery. My aunt, Olga Chmara, was buried there (two separate archival documents name the Coniston cemetery) but her name is not on the marker.
I asked the municipal department in charge of cemeteries what could be done to remedy the overisight. There is no possibility of getting her name added to the bronze plaque, however, I was told that because of the vandalism on the stone, the maker was expected to take the stone back to the studio to repair the damage, at which point my aunt's name could be inscribed on the granite. I did make the request, but it's not clear when the stone would be repaired.
My suggestion would be to dig up death certificates, hospital death and church funeral records, which will be most likely to indicate place of burial.
If you can find proof there that your family member was interred but has been left off the plaque, it's still possible to have the name inscribed in the granite.
Our family left a memorial of our own there (see attached). I hope it has survived the vandals and the elements. For now, it's all we have.