Is it permissible to pay off an old loan, taken to purchase a car essential for work, with a new loan at a lower interest rate, while increasing the amount of the new loan to obtain cash liquidity to pay off another debt, in order to avoid dismissal from work?

It is not permissible to take a car through an interest-based loan to begin with, and entering into another interest-based contract to pay off the first debt is also forbidden, even if the bank reduces the interest rate. One must fear Allah, refrain from usury, repent from it, and resolve not to return to it. For whoever abandons something for the sake of Allah, He will compensate him with something better and provide for him from sources he could not imagine.