If you are honest and upfront with the DOL, I do not think anyone will accuse you of fraud, but you should make sure you document communications, so that you have proof that you are not seeking benefits for the period of time that you were incarcerated.
This answer does not constitute legal advice and you should contact an attorney to confirm or research further any statements made in this answer. Any statements of fact or law I have made in this answer pertain solely to New York State and should not be relied upon in any way in any other jurisdiction. Additionally, we also encourage you to reach out to us via Twitter (https://twitter.com/#!/employattorney) or Facebook (http://www.facebook.com/WhiteRicottaandMarks) if you have follow up questions as we do not monitor questions after providing an initial answer.
As far as I understand your question, I would say it only matters what you say when you call in each week. If you don't call in, you don't get paid. If you call in while in jail, you need to say that you were not available or looking for work.