It all depends on the wording of the STD policy. Usually, these types of policies only require that you submit medical statements from your treating physician(s) in a timely fashion and say nothing about having to maintain a health insurance policy. This is one of those questions where the "contract is king". You only need to comply with the terms of the STD policy. Review your policy carefully, or better yet have it reviewed by a qualified lawyer, to determine if there is a requirement that you maintain health insurance.
It has been 6 days. If an attorney in your area does not respond pick up the phone and try to get your answer. I agree with the fine attorney that did respond, look at the language of the STD
I am an Arizona attorney. AVVO does not pay us for our responses. Simply because I responded to your question does not mean I am your attorney. In Arizona a non-lawyer is held to the same standards as an attorney so there are dangers to representing yourself. This is for informational purposes only and should not be considered as legal advice. If you require legal assistance an in depth discussion of your case is needed as there are many other issues to consider such as defenses, statute of limitations, etc.