I HAD AN AT FAULT AUTO. ACCIDIENT.The injured parties wish to settle case for a one lump settlement.IiF THEY SIGN power of ATTY.will MY INS.pay me?

You should look at your policy, but probably not.  Unless the insurance company is asked and refuses to provide you with a defense to the case (and even then the settlement would have to be reasnable and made in good faith), it is not responsible to pay a settlement to which it never agreed   If you circumvent your insurance company in the setlement process, you must expect that you, personally, will be paying any settlement amount.  If you notify your insurance company properly, it will represent you in negotiating a settlement with the injured parties.  If it winds up reaching a settlement with the injured parties (90%, at least, of such cases will be settled, although not often at such an early stage), it will (assuming that there is no coverage dispute, the settlement is within the policy limits, there is no retention, etc.) pay the settlement.