Next, you need to ask your employer to give you your last paycheck. Most state laws mandate that the company give you the check for the final payout before you leave the office on the last day, while others are a little lenient and state that if the employer cannot give you the check right away, he should at least give you a letter stating when you would receive this check. Don't leave the office with either one of the two; otherwise, you will end up spending weeks chasing the accounts department for the money due to you and waste your valuable time that should have actually been spent scouting the job market. Also, check whether you have been paid for all the days that you worked until the last day at your job and that all the accrued paid leave has been accounted for. Don't be shy to point out any discrepancies in the calculations; you'll need every penny that you could get from your employer.
Further, your health insurance is important. Hence, get details about COBRA before your leave the office premises and understand from your HR manager what you need to do and who you need to contact for continuing your health insurance between jobs. This is very important as you never know when something may go wrong and you may need your insurance to cover it.
Next, your W-2 is important. So, if your employer defuncts and then is nowhere to be found, get in touch with your local IRS office. If you give them a copy of your last paycheck for that tax year, they could give you a substitute W-2.
Also, if you were given stock options, do not neglect them. Sure, they won't be worth as much as they were a few months back, but then they wouldn't be completely worthless either. Get some help from a professional financial planner and sort out your stock options. The money they bring in would certainly be worth the effort especially if you do not have much saved up in the bank.
Finally, get in touch with a career counselor or a professional recruiter, spruce up your resume, and start looking for a new job. Don't say no to exploring any opportunity that comes your way. At least interview for it, and after that, if you still do not like what's on the table, you can definitely say no to the offer. In any case, see if you can get some consulting work when you are unemployed, even if it's for free. This will ensure that you do not have a gap on your resume and stay current with your vocation.