jiffy lube put in the wrong filter into the car which made my engine have no oil, sue? yes? no?

so about 3 months ago we go to jiffy lube to get the oil changed, and the other night we we driving the car and suddenly the check oil light came on, took the car to a machanic and figured out that they had put on the wrong filter for the car, mechanic states the car had been running on low to little oil. so the mechanic advised us to either sue for future issues with the car for the full lifetime we have the car, pay for a new engine or have them pay off the remainder we have on the car (8,000).
the car is a 2001 audi a4 quattro so any option would really be costly to them(jiffy lube)
any other options or advice would be helpful - Is this your question? Add additional information