Be honest about everything. In most cases, you will not have to take your 401K out because of the tax hit. However, in most cases, you can take a small amount of money out of it and have your accountant put an addendum with the tax form that it was for job loss or illness, whatever. I did that and it worked out fine.
Also, try food pantries. Shop at smaller community ethnic stores. You can get an amazing amount of fruits, vegetables and meat if you are willing to stay away from the big box stores.
I was on welfare and reported when I went to work. For six months after, I was sent food stamps. I called the case manager and she said that it was factored with my new income, not to worry.
Two years later, I was summoned to HR at the hospital I work with a notification to appear in court. They went though my employer. I was mortified. I had to pay back everything they gave me in "error" for the six months--over $5,000. Also, they took my State income tax refunds for five years.
Be honest. In today's computerized world, our information is just a click away.
Take the help you need, that is why it is there. Just be sure to play by the rules.