Why should mother die intestate?
It's really quite simple to draw up a valid will. There are many websites that can help with this, but getting proper advice in the real world doesn't need to be that expensive or difficult, and you should go for it. The possibility also exists, for example, of creating a trust which allows youngest daughter to continue to live in the property until it is sold.
Dying intestate means that surviving relatives face months or years of legal hassle. If those survivors are already living in reduced circumstances, it can make their situation next to impossible.
Unless you're talking about a house with an outstanding mortgage or other charges on it and/or a very argumentative family, I see no reason why that daughter shouldn't stay where she is.