It is not a legal requirement for a person to make a Will but very silly of them not to when there is property and/or a vast sum of money involved. When someone dies intestate (without leaving a Will) the next of kin can apply for a Grant of Representation. This is issued as Letters of Administration and it is in their hands to see that those entitled under the law of intestacy receive the proceeds of the Estate. Where there are no living relatives, the Estate goes to the State. Where there is a Will but those mentioned as beneficiaries are no longer alive, and no mention of what is to happen if they pre-decease the Testator or no Codicil has been added, the Solicitors handling the Probate will use various means to try and find descendants. I know this from experience from working in the Probate department of a Solicitors for years.
It is also not a legal requirement for any notice to be placed in a newspaper(s) in Ireland, but it is normally done to make people aware of the death and give details of the funeral. I know this from experience as my husband was born in Sligo and all his family still live there.
But remember, not everyone makes a Will. We have had fairly young relatives die, who owned property and had a fair amount of money in the bank, but never made a Will due to their young age and not thinking it was something which was needed till later in life.