It depends on your circumstances, and on such things as the age of the child and notice (i.e. the utility would have to be notified properly, if you are claiming special circumstances.)
You may want to look at http://www.massresources.org and call your local state agency.
Do you want accurate, personalized, legal advice that you can rely on? You will have to hire an attorney, not ask on Avvo.
I am not your attorney and am not creating an attorney-client relationship by this post. I am therefore giving only general advice. This advice may not apply to you or your situation; may not take account of all possibilities, and may not match the advice I would give to a client.
DO NOT rely on this advice or any other advice on Avvo to make your legal decisions.
If you want an answer to a legal question you should retain an attorney who is licensed in your state.
Oil companies are not regulated monopolies like the gas and electric companies. They can refuse to do further business with you until the outstanding balance is paid. You can try to do business with another supplier.
Disclaimer: This site exists to provide information only. It is not legal advice. Answering your question does not create an attorney-client relationship. I am a Massachusetts lawyer. Any information provided on this site does not, except as explicitly stated, imply familiarity with laws or procedures peculiar to your state which may differ from those where I practice.