It's possible that your loan company will modify your existing car loan, specifically by extending your loan term, lowering the payment for several months, etc. You can call the lender to discuss your options, especially if you have recently had a hardship such as a job loss or divorce.
Please be aware that as with any loan, any type of modification may damage your credit (in this case, a loan modification is technically a breach of contract with the lender, and for this reason your scores could be affected).
It is not very common to modify a car loan. Instead, most people refinance, which does not hurt your credit scores. If you cannot qualify for a refinance, however, loan modification may be a good option for you.
So do your homework ahead of time. There may be cheaper options, such as refinancing. Get a payment quote for an extended term loan with your lender and compare the rate and terms to refinancing with other lenders.