france
Alice cannot quit on the spot (with some exceptions related to health and safety which do not apply here). There is a notice period to do so (the legal maximum and most common is three months), during which she must still follow her employer’s instructions, as long as they are legal and fall within her job duties. ("Her job duties" are outlined in her fiche de poste, a legal document that forms part of her work contract and cannot be changed unilaterally.) What happens next depends on how she breaks the law.
If she physically leaves the company never to work for them again (with or without invoking - wrongly - one of the "health and safety" exceptions as a justification), her employer may ask for damages under article 1237-2 of the labor code ("abusive severance of work relationship at the employee’s initiative").
Outside this cause of action, things are more difficult. What if she stays on the premises, performs other work duties, and otherwise does her job except fixing the bug? Suing Alice for damages for actions done (or not done) within her job duties requires that Bob first fires her for heavy fault (see e.g. Cour de cassation, Chambre sociale, 7 mai 2024, 22-23.180, §5-10).
Firing under French law is (almost) always for-cause, and falls under three categories of gravity: simple, grave and heavy fault. The latter category requires that (1) the employee acts in such an egregious manner as to "make impossible to keep the employee within the company for any duration of time", and (2) the actions reveal an intention to harm the company. The typical examples are disgruntled employees deleting documents, vandalizing company property, etc.
It is very unclear to me that Bob could successfully prove that Alice’s behavior meets the heavy fault standard. She is not taking overt actions to destroy company property, and she might not have communicated her blackmail explicitly. Alice failing to fix a simple bug due to incompetence is at most simple fault; Alice asking a bonus is not grounds for termination.
Bob also needs to act promptly. If Bob decides not to fire Alice immediately for some reason, then has a later change of mind, it becomes difficult to argue that her actions meet the first prong of the heavy fault standard ("actions so egregious that she cannot be kept as an employee for any duration of time"). Bob could potentially show that he did not understand the gravity of Alice’s action at the time (maybe senior engineer Carol, who eventually fixed the bug, comes up weeks later with irrefutable proof of points 2 and 3), but that muddies the waters.
Assuming Alice is liable, then she is on the hook both for recovery steps (say, if the company needs to hire an external consultant on an emergency fee to fix the bug), and money lost due to the bug past the point she could have fixed it. Proving the exact timeline might be a tricky factual question, of course.
