Does being terminated qualify as loss of livelihood for tax exemption for 1099-R distribution?

Unemployment doesn't mean you can withdraw early unless you were over 55 when you left your job and your distribution was from a 401(k). For 2024, there's an exception for distributions up to $1,000 for an early withdrawal from an IRA. or 401(k).  Once you enter the distribution, TurboTax will ask you a series of questions to see if you can get the exception.

Refer to the TurboTax articles: What are the exceptions to the penalty for an early withdrawal from my 401(k)? and Are there exceptions to the early distribution penalty on an IRA?

Refer to ‌IRS Topic 558, Additional tax on early distributions from retirement plans other than IRAs for  information on exceptions to the 10% additional tax.