Right. You do not even have to report this money to your unemployment system. Ever. Do not try to report it on your weekly or bi weekly certification. They may have a question about "are you drawing or did you begin to draw...." regarding pensions, but that only refers to whether or not you were approved for SSDI this week or whether you began this week to draw a company sponsored retirement or disability pension of some type. Your 401K is NOT that kind of pension. That's not what that question means. Do not mark it "yes," unless you want a long delay in your weekly checks, after which they'll tell you the same thing I'm telling you here now.
They want to know if you did work for which you have been paid, or will be paid in the future, and if you did, how much wages were you paid this week. They don't care if you won the lottery, sold your car, if your grandmother's estate came through with $50 million, if your wife got a better job.
They did not use your income to decide whether or not you were eligible for unemployment, and they do not give it to you based on your being low income or not having money to live on.
But if at all possible, you should avoid getting out your 401K, because of the terriffic tax liabilities you'll have at the end of the year. And then, too, unemployment benefits are taxable, and you'll actually owe taxes on them unless you are already having money taken out each week. Even if you haven't found another job.