Here's the deal. In CA, the odds of your 401K withdrawal affecting your UI benefits is very close to zero. However, Commentator makes the best point that reporting it this way will trigger an investigation and suspend benefits which will stress you out.
However, this method works in every state so that it NEVER affects your UI benefits, and requires no reporting to any UI agency. You take the 401K, and you trustee-to-trustee transfer it to an IRA, and then withdraw from the IRA. Credit Unions typically have the right kind of IRA accounts to make this convenient, easy, and relatively fast. The big banks, not so much. However, Commentator telling you to leave it alone is probably the first choice.
Since it sounds like you put the money in your pocket and can't now opt for the trustee-to-trustee transfer, you can take the amount from your own funds and deposit it into an IRA as a rollover provided your in the 60-day window to do this, and turn around and pull it out the next day an accomplish the same goal, but you'd still need to make up for the 20% that was withheld because you didn't ask about what to do BEFORE you went and did this on your own.
The other reason to do it my way is because a lot of times people don't need all their 401K plan money. These credit union accounts I mentioned allow for on the fly withdrawals. If you end up getting another job, you can take the remaining funds still in the IRA and maybe move it into your new employer's plan, or invest it in something with a better rate of return that's less liquidity. The point is that it's a way to try to preserve all the hard work you did saving for retirement instead of starting from zero. While not relevant for a claimant that gets let go at the beginning of the year, it can result in a huge tax savings for someone let go at the end of the year. In that case, you've worked mostly the whole year, and people take these huge 401K withdrawals and pay the highest marginal tax rates. By putting it in an IRA, they can mayme wait until after Jan 1 to do the IRA withdrawal and if they're out of work for a long time with nothing but UI, they can drastically reduce the tax hit by shifting the "income" into a lower income year.