If You Are Receiving Unemployment Benefits. Can You Take A Distribution From Your 401k And Still Receive Your Unemployment Benefits?

It won't affect your unemployment benefits.  As far as that is concerned, it would be like taking money out of your savings account.  But, as Dannybooks said, you'll be responsible for taxes on the income plus a 10% penalty on the withdrawal.  You have to weigh the results against the amount you withdraw to see if it's worth it.

I ran into this and called EDD in California. For me, as long as I paid into the 401K in the past, a taxable withdrawal did not affect my unemployment

It ABSOLUTELY can affect your benefits. Check with your state's guidelines to be sure of all questions you may have. Certainly you should never ask questions on-line of this importance. In Minnesota, it absolutely
counts as income, and your benefits will be reduced by that amount. You need to roll whatever money taken out into another "approved plan" - either an IRA or pension plan. ASK THE STATE you live in (again), do not rely on sites like this for important information!!!!