It depends on whether the property passes via probate or not. For instance, if the decedent held all property as joint tenants with right of survivorship with another individual, then there may not be a need to start probate; but there may be a need to file an inheritance tax return. So, the first step is to determine the type of assets owned by the Decedent. Assuming that there are one or more assets owned by the Decedent in his/her name or there are assets that pass to the Decedent's estate, then probate needs to occur. If there is no will, then whomever are the legal heirs have to agree on who will serve as the administrator of the estate as each legal heir as an equal right to serve. For instance if the Decedent died a widower and had four children, each of the children has an equal right to serve. In the event they cannot reach an agreement then a petition has to be filed. So, once you have determined whether probate needs to occur, or not, you need to seek out the advice of a probate attorney on what actions to take.
Mr. Bernick offers a good summary. Probate assets pass via the laws of intestacy and that depends on the relation of the deceased to other family. Non-probate assets pass via joint ownership or beneficiary designations. Having no will can be more costly. This is because someone has to go through the process of having an administrator named, getting a bond, etc. The cost of doing a will, at least a simple one, will certainly save at least that much in the end in my experience.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
Attorneys Bernick and Zelinger have given good insight. I am writing to add the following point for your neighbor: one reson to have a Will is to make sure that an Executor is named, and your neighbor can decide which person she believes to be the most trustworthy and capable of handling the estate and making sure that the estate is divided properly. Also, if your neighbor wants to make special gifts, or make an unequal distirbution of her property after death, these wishes or intentions can be described in a Will, and be enforceable.
There are many reasons to have a Will, and your neighbor should not be afraid to talk to an attorney about how her proeprty should be administered and divided after her death.