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No. Although the law gives employers a great deal of leeway in deciding whether to fire an employee, there are limits. State and federal laws prohibit employers from firing workers for certain reasons -- for example, because of the worker's race or religion, because the worker took family leave, or because the worker complained of illegal company activity.
If the employee has an employment contract or you have made promises to the employee, then you must honor your commitment. Typically, this means you cannot fire the employee without "good cause."
It depends. The law does not require you to give severance packages to employees whom you fire. However, if you ever promised the employee a severance package, you should deliver on that promise. And if you ever signed a contract with an employee in which you agreed to provide a severance package, then you must honor that contract.
Sometimes, you might be willing to give a fired employee a positive reference. After all, an employee who wasn't a good fit at your business might do well elsewhere. If you can say positive things about the employee, then say them.
If, however, you are not comfortable giving a positive reference, then you shouldn't. In such a situation, less is better than more. When prospective employers call, tell them that you can only confirm dates of employment and job responsibilities and no more. You must take care not to "trash" the employee to a prospective employer, because this will leave you vulnerable to a defamation suit from the former employee.
In many states, yes. Failing to fire an employee who poses a danger to coworkers, customers, or others can lead to a lawsuit for "negligent retention." For example, if you hire an employee to make deliveries to customers' homes, and that employee has a serious criminal record that you failed to check, you might be liable to a customer whom the employee robs or assaults.
For more on your responsibility for employees' conduct, including tips on avoiding claims of negligent hiring and retention, see Employer Liability for an Employee's Bad Acts.
Under most "whistleblower" laws, it depends on the employee's intent. As long as the employee has a good faith belief that something illegal is going on, you cannot fire the employee for complaining about it. If, however, the employee knows the complaint is false and makes it simply to stir up trouble, the employee probably is not a protected whistleblower.