Can you jettison a project to work on another in the wake of a big discovery?
Can Alice ditch her project to work on the new discovery? 


Alice has many responsibilities in her life, including satisfying her sponsor and producing her thesis. Whether she should ditch her project depends on those responsibilities. IMO, she perhaps doesn't have enough time to fulfil her obligations and ditch her project (PhDs are short), so she might need to delay working on the new discovery. There's perhaps an exception if Alice is in the early stages of her PhD.


  What if the new discovery is in an area that is not her supervisor's
  specialization? 


That's not particularly relevant: Many students work under the supervision of advisors that aren't specialists in their research areas.


  if she's a professor (as opposed to PhD student).


Then, she isn't bound to the time constraints of a PhD, but still has other responsibilities.


  I'm also curious whether Alice can make this decision


Yes, she can. Who else would make it? Pressure may be applied by others, but, ultimately, the decision is Alice's. (That said, she may get sued for her decision, e.g., if she ditches her project without delivering upon contractual obligations, but that's perhaps unlikely in academia, even less-so for student-Alice, as opposed to professor-Alice.)


  I'm also curious whether Alice can [feasibly] make this switch if she's a professor (as opposed to PhD student).


If Alice truly wants to switch, then Alice can make it happen. There may be many barriers: personal, institutional, contractual (including funding obligations), ... But, they can be overcome. That said, should she switch? That's up to Alice. She perhaps has a relatively easy position right now, switching will be a massive upheaval.