Can an employer force an employee to quit in order to rehire them back as an independent contractor?

Can an employer "force" an employee to quit? No, the employee could refuse to quit, no matter what. Of course, unless the employee has a written employment contract guarantying his/her employement or limiting the reasons he or she could be terminated, the employer could simply terminate his or her employment if the employee refuses to quit. However, since if terminated but not "for cause" (e.g. not for insubordination, theft, gross negligence, etc.), the employee may eligible for unemployment benefits--whereas if she or he resigned, even at the employer's strong urging, he or she would not be able to receive unemployment; therefore, there may be an advantage to refusing to quit and making the employer terminate.

In answer to the rest of the question: employers may dispense with some or all employees and instead use independent conrtractors, BUT unless they truly meet the test to be indpendent contractors, they will still be employees (and must be paid, etc. like employees), no matter what the employer wants to call them. You an find the test or criteria for when someone is an independent contractor vs. an employee on the U.S. Department of Labor website and also find almost identifical criteria on the IRS website (any differences are due to the two agencies' different missons and perspectives), but the short answer is, if an employee is fired and rehired as an "independent contractor" but does the same job, in the same way, over the same or similar hours, and subject to the same supervision, he or she is almost certainly still an employee and must be paid for all hours worked and overtime as applicable; would be eligible for employee benefits; the employer would have to withhold salary for taxes; etc.