There really aren't any parts that are "likely" to fail but areas of concern would be things like--1. When was the timing belt (along with the water pump and attendant idle pulleys) changed? If never, now is the time. It's relatively costly service but a failure in that area will cause massive damage to the motor. The heart of the service is a rubber belt that wasn't designed to last forever.
2. What is the age of the battery. With winter finally upon us an old (5-6 years) battery is more likely to fail.
I think your Mom's best protection is having a competent, honest service person examine the car periodically--say every 4 months--which would include a close look under the car (to visually inspect brake hoses, pad wear, exhaust system and hoses, etc) and a thorough road test. A competent mechanic will look, feel and listen to how the car drives. It may cost a few hundred dollars per year to do this but a trustworthy service person examining the car is your best insurance. -- Dave