Is it fine to threaten an employee like this?
No. It's actually a crime (StGB §240 Nötigung).
If they can do it that way, what are the consequences?
They absolutely cannot. Ending an employment contract immediately (BGB §626 Fristlose Kündigung) is only possible if there are facts that make continuing the employment to the end of the notice period "intolerable" after considering both sides' interests. Generally, this applies when
the employee substantially violates the contract or intentionally does something damaging to the employer. Examples would be working hours fraud, sexual harassment of colleagues, or passing business information to a competitor. Errors or mistakes, no matter how critical, pretty much never fulfull this criterion.
How should I react to this threatening?
Record everything. If it's not in writing, create detailed meeting notes (i.e. what they said, when, where, in what context). Insist on written instructions for everything that might be construed a breach of contract, like "you don't have to come to work tomorrow". Do not give in to the threats, don't sign anything, but do start looking for a new job, because you sure don't want to stay in such a toxic environment.
I'm pretty sure they know they don't stand a chance, so the most likely outcome is that they'll fold and keep paying you until the end of the notice period. If they really try to go through with it, consult an employment lawyer.