The answer is almost surely yes.
There may be some exceptions for public or government employees, depending on what they say, because some protections arise for public employees provided that what they say regards a matter of public concern and the statement is made in the capacity of a citizen rather than an employee. The difference is complicated. But for persons employed by private companies or corporations, what they say on Facebook about their employers can be used as proper and lawful grounds for termination of employment, although there may be exceptions.
Lexington, Kentucky employment lawyer Robert Abell represents individuals and employees in employment law cases including wrongful termination and discrimination cases; contact him at 859-254-7076.