If you lose your job, you will likely still want to keep up with your retirement savings in order to secure your future. While you cannot add to a 401k once you've left the job, this doesn't mean that you are out of options. If you have savings or leftover money from your unemployment checks, you can still invest it.
What to Do
Since you can't add money to your 401k as it is, the smart thing to do is roll it over into an individual retirement account (IRA), which may allow you to make contributions. This process simply requires opening an IRA and transferring the money directly to the new account. Another option is to let the 401k sit where it is, transferring it to a new 401k when you get a new job that offers one.
Married vs. Single
If you're single, you cannot contribute to an IRA unless you have earned income. Unemployment or disability payments do not count as earned income, even though they are taxable. However, if you are doing some freelance work on the side while looking for regular employment, you can contribute this money to your IRA. If you are married to a someone who's working, you can contribute up to the $5,000 maximum amount ($6,000 if 50 or older), provided your spouse makes more than that.
The disadvantage with retirement savings is that there are often penalties for withdrawing the money early. When you don't have a steady source of income due to lack of employment, you are in a precarious financial situation. Rather than worrying about your retirement savings, it's smart to save up six months to a year's worth of expenses that you keep in an account that's readily available. Only look to the distant future if you already have an emergency fund.
Investing While Unemployed
If you have an emergency fund saved up, but still have extra money and are either ineligible for IRA contributions or have fully funded your IRA, you can still invest your money. However, not in accounts that have the same tax-protected status as retirement accounts. Consider investing in certificates of deposit (CDs), which you can purchase from your local bank, or open an account with a brokerage firm to purchase stocks, bonds or mutual funds.