if there's a remaining family member and they inherit according to the will: they cannot sell without first going through probate.
They can attempt to sell by pretending to be the owner but this is fraud - any solicitor must satisfy themselves that the seller is in fact the owner of the property. They can, and do, ask for passport or other identification. Title deeds are necessary also.
If they do not want to sell or do not need to, the property can remain in the deceased's name until the property is to be transferred.
A buyer does not really know if any problems exist until their solicitor checks everything out. Sales can fall through when it is discovered all is not well.
Checking 'good title', is one of the crucial duties of your solicitor and why its always advisable to retain one.
Next scenario: No relatives.
The property falls into the ownership of the State. Any living relatives who subsequently appear can apply to the authorities to inherit.
If the State has not taken over the estate and it's in some sort of abeyance, then get a local solicitor to investigate for you. There is also the possibility of some other neighbour squatting on the land but its hard for them to establish ownership. And can provoke rows in years to come.
According to law, all costs associated with the winding up of the estate including burial must be paid first. Then, any mortgages or liens on property - these will be written on title deeds. Then any non-secured loans.
Mortgages must have life insurance attached so the mortgage is repaid on death. Other loans also often have insurance.
Nowadays, they take as long as necessary - maybe someone returning from Australia, California etc. For example, I am going to one next Thursday, the man died last Saturday. But he has children abroad.
Post-mortems can prolong things too. Also, delays at graveyards or crematorium can dictate. And lately, the lack of priests has sometimes delayed by a day or two.
A priest told me years ago that the three day rule was to do with Christ's death and resurrection - 'He rose again on the third day' etc.
You'd really be better off talking to a local solicitor in Sligo about the more technical legal stuff. Google them and you can talk by email.
Hope that helps,