The lack of a probate creates a cloud on the title. No one has legal title. The property cannot be sold or mortgaged until the title is cleared. The estate must be probated in order for legal title to pass to the heirs.
There is no executor of probate. The executor of the estate executes the will and probates the estate.
It will be dependent on how the first will was written, but in most cases, their share of the estate simply becomes a part of their estate.
If the person left a Will the Will will identify who the administrator (executor) of the estate is to be - only this person can anministor the estate. If there is no Will then the state will appoint an administrator (there will be country specific laws relating to how this happens).
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You become one of the creditors of the estate. Whether you receive anything depends on the size of the estate and the size of the claims on it.
Their share goes into their estate.
The government is not going to get their money. They will have to be satisfied that there are no assets in the estate and that no one else got paid.
Debts are one of the primary reasons someone should open an estate. The estate has to pay off the debts. If the estate cannot do so, they distribute as best they can. If the court approves the distribution, the debts are ended.
The estate will have to sell or abandon the home.
If any undistributed assets remain in the estate then the estate must be reopened and an estate representative must be appointed by the court.
Someone else will be appointed the executor. The probate court will appoint someone, usually a bank or attorney, if no one 'volunteers' to do the work.
The estate will be distributed according to the Pennsylvania Intestacy Statute.