This is difficult and heart breaking.
From what you have told me, it would seem that she is not producing excess saliva, as perhaps having difficulty swallowing her saliva. (please advise if this is not the case).
Your parents could make up a saline solution, of warm water and salt, and use a syringe plunger to inject the solution across her teeth and gums after eating. This would help remove some of the food. By placing the syringe in the corner of the cheek (facing towards the front of the mouth and ensuring the cats head is no back, as we don't want her to choke on the solution), gently and slowly expel some of the saline solution from the inside of her cheek towards the teeth.
A warm water solution and cloths can be used to wipe her face, legs and chest to help her keep clean. Adding a cleaning substance to the water, may be too much for her to tolerate, the foreign smells and cause her further distress if she attempts to clean herself, so I recommend, just plain warm water.
I would consult the vet for any topical products that may relieve any pain in her mouth that may be preventing her from swallowing. If she is suffering, there may also be a systemic analgesic that may also help her.
Another possibility is to try her on increasing liquid substitutes. There are various liquid formulas that your vet can recommend. Many cancer patients end up having to supplement their diet with liquid nutrition. Also, this may not be viable, depending on how well she is able to drink, as if she cannot swallow her drool, this could be a problem. I don't know how she would go drinking from a baby bottle.
The only way, I can see, is for her to have this careful regime 3-4 times a day to help keep her as clean and comfortable as possible. It sounds like she may not have a long time in this state, as she will eventually be unable to chew and swallow food. So this can offset the difficulties of caring for her, knowing that it won't be for a very long time.
If she is unable to swallow properly, be sure to keep checking that she is not dehydrating, as this is a painful condition, and if these types of complications cannot be managed, it can sometimes be kinder to take the hard road of euthanasia.
I do not say this lightly, and hope she is able to have some comfortable months and your parents are able to enjoy her.
I have not recommended specific products, as I'd prefer to see her vet do this.