Quite correct, as I have discovered! I have a family member buried in the family grave in the Borough Cemetery who is not honoured with an inscription - and I only found out about her presence by accident! Bit of a shame really, because she purchased the grave!
The other possibility if you are in England is that the person was buried in a "public" grave. I have a mother and son buried together in a "public" grave in London, which must have consisted of rows of metal numbers in the 1930s. It is now a well developed wood littered with metal numbers and the odd memorial pot. I don't know whether the Island indulged in a similar activity!

James