In 2002, after receiving a green Card in the USA I got SSN. In America I never worked and left it. I live in Russia , the green card was for two years. Have not been there for 14 years. But in 2002-2005 my SSN was used to get payments through the sites. As far as I know, IRS sent the claim to the old address in the USA many years ago then stopped ( I think they were told I don’t live in the USA anymore, useless to search for me ) Plus I thought why pay not living in the country where I can’t even go. My Question is there a statute of limitations. If i go there will I have any problems in the USA. Should I pay or need to explain them? 

First, once you have a green card you are taxed on worldwide income for US tax purposes. Failure to maintain a green card by staying in the US is an immigration issue but not a tax change. So you need to formally abandon your green card by taking affirmative steps [filing Form I-407] or by other written means. Second, there is no statute of limitations on returns that are not filed. Therefore, please seek good tax legal counsel to advise you on this.

Eric Rothenberg