Money left unused in your FSA goes to your employer after you quit or lose your job unless you are eligible for and choose COBRA continuation coverage of your FSA.
Even if you’re able to continue your FSA with COBRA, your FSA money can’t be used to pay for monthly COBRA health insurance premiums, nor can it be used for non-COBRA health insurance premiums such as those offered through each state’s health insurance exchange
If you’re not eligible to continue your FSA via COBRA, you’ll want to try to use up the money in your Flexible Spending Account before your job ends so you don’t lose the money.