The executor of an estate is the only person who can distribute the money in a certain bank account of the niftar. There is a possibility that the money was being watched for another party by the niftar. In addition although we don’t really know who that other party is- one of the yorshim knows who that party might have been, but thinks that it was the niftar’s just he wanted the children to help that other party should she need help. She never turned to the yorshim. There is no way to verify it, and the yorshim are mesupak. May the yorshim take the money- is there a midas chassidus to give it to anyone?
Even after a person appoints an executor over his estate, the yorshim — the Torah inheritors — remain the owners of the property after his death.
In the absence of any concrete instruction, there is no obligation on the inheritors to give anything to anyone [even if an instruction was given, the obligation is only incumbent under certain circumstances — but there would at least be a midas chasidus], assuming of course that the estate belonged to the deceased.
If somebody else wishes to claim the estate, he must make a claim for it, and prove that the property is his. Merely “a possibility” will not obligate the inheritors, who are muchzak (in holding) of the estate to give it to anybody.
Therefore, based on the information given, the inheritors will not have any obligation, and will be able to keep the inheritance for themselves.