Is it a biometric passport? (I'm guessing yes, given her age) Even if they are identical twins they will have different biometric data on the passport. Fingerprints and irises differ despite the fact they are twins.
I personally wouldn't think about the fact its illegal. That wouldn't be my concern. You might get or a punishment, you might not.
But if its a passport I would think about the consequences of if its picked up - regardless of being guilty or not guilty; practical stuff that has a long term impact on your ability to travel or work in the future. Stuff you wouldn't really think about.
If you get 'flagged' for some reason, you will always face issues at passport control and if you are deported or refused entry to somewhere it can affect whether you are allowed entry to somewhere completely unrelated and different (you are often asked on landing cards if you have ever been refused entry somewhere).
Personally I ask is it worth missing out on lots of other future opportunities for the sake of this one when all is said and done? If she can't find the passport, then she should suck it up and use it as a lesson to look after the passport - and not properly jeopardise her future.
Not to mention her sister's future too. Her sister who has NOTHING to gain as she won't be going on this trip, and potentially everything to loose if its spotted. In a situation where she did get caught and took full responsibility for the 'theft' of her sisters passport, her sister's passport would still be 'flagged' as such.
She does not NEED to go. She is being being immature and selfish for even considering using her sisters passport. Thats the bottom line in the end, I'm afraid.