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There are potentially "hardship" withdrawls allowed due to heavy financial need, as well being able to borrow against the 401k and then paying yourself back. You have to judge which works best for you.
You can also determine what your tax liabilities will be. Often the 10% penalty may be offset by your tax bracket, exemptions, deductions, child tax credits, etc. so that you don't actually incur an out of pocket cost for the penalty. Talk to your tax professional.
Here is the IRS link to hardship distribution of 401k:
http://www.irs.gov/retirement/article/0,,id=162416,00.html
Personally, I would prefer to tap a 401k for $11k if I could get back on my feet, working and avoid BK. I would not go BK strictly to avoid tapping into it. The cost of bad credit in the future will cost you more than $11k in extra interest and costs associated to any type of credit you use for the next several years (auto, mortgage, etc).
However, do make a detailed budget, cut the non-essentials, buy generic/store brand, sell unnecessary and unneeded items to supplement the budget too in order to give you as much cushion as possible along with the 401k.