As long as they need. There is limit to the time a person can be investigated. The New York Department of Labor which administers the UI Program has a special hotline and unit dedicated to investigating UI fraud. The DoL actively investigates these matters and works closely with the county district attorneys and the New York State Police.
For example, in late 2009 and early 2010 the DoL, various district attorneys and the NYSP arrested 53 individuals in the three upstate regions for theft of nearly $250,000 from New York State's Unemployment Insurance trust fund. It was highly publicized. And as noted above, the State Labor Department worked with nearly every district attorney in these regions, as well as dozens of other law enforcement agencies. And as also noted, most of those arrested had collected UI benefits while earning a paycheck.
In fact, New York's stepped-up crackdown on Unemployment Insurance fraud saved businesses large and small more than $35 million last year alone. (a State claim not Mine)
So you can read between the lines on how aggressive enforcement of this is.
The Governor directed the Labor Department and its partners in law enforcement to remain aggressive in bringing individuals who defraud the UI system to justice. This fact has been widely publicized. I assume Governor Cuomo (the Former AG) will be no less aggressive.
The Labor Department operates a program that emphasizes improved detection of fraud through data matching, more proactive investigations and better coordination with local law enforcement and prosecution agencies. It also has a fraud hotline.
The only remaining issue I see, remain is the amount involved and a possible statute of limitations for prosecution. The techniques could be any legitimate investigative tool available to law enforcement. It could be personal interviews, subpoena of records, including bank records, surveillance, etc.
And it goes without saying, criminal sanctions can be varied including probation, jail and most certainly restitution. Needless to say, a fraud conviction may very well prevent future benefits. However, on that issue my colleagues may wish to comment further.
If this answer was helpful, please click on the "thumbs up" link.
Disclaimer: This response is for informational purposes only. It should not be construed as legal advice or creating an attorney client relationship. As with any evaluation of your legal rights and responsibilities, I would urge you to speak with an experienced attorney in your local for definitive legal advice.