Hardly. It depends on the settlement. Full payoff and no job as a manager for six months (or whatever) or partial payoff and no work restriction. It’s a contract between two parties that they agree to and abide by. Mancini had a contract with Inter with three years left when he was sacked so there would have been a lot of intense discussions to settle that one!
No.
Either you’re not fired, carry on as an employee on gardening leave on full salary.
Or you receive a pay off (whatever the amount) and your employment is terminated.
No employer can make you sign up to a period of unemployment. Even non-compete clauses are incredibly hard to enforce.