If your family member lives in Texas, the "next of kin" will be determined by the Texas laws of Descent and Distribution. In this context, we sometimes refer to them as "heirs" or "heirs-at-law." By definition, heirs are those people the law recognizes as beneficiaries of a person's property when they die without a will.
The heirs of any given property will vary depending upon what type of property your family member owned. More specifically, whether she owned real estate and/or personal property and whether such real estate and/or personal property was her separate or community property. All of these questions should be thoroughly discussed with a competent estate planning and probate lawyer as there is no easy way to answer your question here.
The Texas Board of Legal Specialization hosts a website at www.tbls.org wherein you can search for a lawyer that is board certified in estate planning and probate near you.
Without tracing this lady's personal family tree to determine who her heirs will be, this is a hard question to answer. In general you look first for a spouse and children. If there are none then you look to see if there are descendants of any children. Then if you still haven't found anyone you go back up to the parents and then out to the siblings and their descendants. You keep looking until you find a living heir.
If the lady is still competent you could make a Will. Feel free to call the office if I can be of assistance.
For educational purposes only. No attorney-client relationship was created by this communication.