What shade did she buy?
I read that the shade "SHADE" seems to smurge badly but not the rest. But so far i don't have problems with any shades.

IMO, it won't smudge and is easily remove using normal eye makeup remover. and the tip is just nice to apply a nice line along the lash, not too soft and shaky like Loreal liquid eyeliner.

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"Early to bed and early to rise, makes a man healthy, wealthy and wise." -some dead guy.

It is also possible that she is applying too much of the liquid eyeliners which are flaking! Have you ever seen her how does she apply the eyeliner, i guess you should only then you would know if the eyeliner is flaking or not....

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It clearly shows that she can't continue to use the same eyeliner being as ineffective and useless, she should obviously look for another eyeliner and this time, she should see to it that she saves some money to buy a good quality product.

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"Love built on beauty, soon as beauty, dies."
-John Donne

I would advise you to use a pencil as eyeliner instead of the liquid one. The liquid tends to peel off unlike the pencil one that sticks to the skin. It can reduce with time but never peels off. Buy a pencil; older means are better and reliable.

Not being an expert in make up stuffs and moreover the eyeliner, i think you should change your eyeliner brand for a new one, this tme, make sure to look for the best one, ask your friends which brand do they use and last longer without flaking! In this way, you would get the perfect eyeliner.