It is not really clear from your question all the information necessary to answer your question. Was there a will from the person who died? Are the children of first cousin the children of a living first cousin or deceased first cousin?
If the person who died did not have a will, and there was no spouse or children, and if there are no living parents, no living brothers or sisters, no living nieces or nephews or their descendants, no living aunts or uncles, then first cousins would be next in line.
As this gets quite complex, you should consult a probate attorney in your area.
This answer does not constitute legal advice nor form an attorney client relationship. I am not your lawyer. If you have a legal issue in Tennessee you may contact me for a free consult.
I agree with Jon's answer. If there is no will and if first cousins are the next of kin as defined under the laws of intestacy, then the children of a deceased first cousin would take that deceased cousin's share.
LEGAL DISCLAIMER-An attorney can only give you competent legal advice if he or she knows all the facts and is licensed to practice law in the state specific to your question. The comments above are not intended to be legal advice but general comments based on the limited information provided in the question. I am only licensed to practice in the State of Tennessee.
It depends on whether there is a Will or not. Matthew Duggin is a probate attorney in Knovxille can probably advise you. His number is (865) 357-9988.
If you would like a consultation, call (865) 522-9000 to make an appointment.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for advice regarding your individual situation. We invite you to contact us and welcome your calls. Contacting us does not create an attorney-client relationship. Please do not send any confidential information to us until such time as an attorney-client relationship has been established.