The catch-all of "Bringing the company into disrepute" will probably cover it. I would imagine she will be allowed to go quietly and keep her pension if she doesn't dispute it.
I don't think any company can sack you without giving you your accrued pension - it's a bit like theft. You have earned that money, exactly as if it were salary and to take it away is now illegal. It used to done but has been stopped. Where this gets more interesting is with a final salary scheme - as you pensionable salary is based on recent past, demoting them reduces not only their basic pay but also limits how long they can stay in the company without reducing their pension. Often people will resign before taking the double pay cut.