If employees don’t follow quarantine rules, can they be disciplined or even fired?

The employer should try to talk to the employee, investigating in the same way the company would for any claim made by someone about someone else — including coworkers. Discipline or termination based on a bit of (potential) rumor/gossip is not advisable. Depending upon which state the company is located in, the company generally doesn’t have the authority to control what employees do in their personal time. The company may, however, prohibit the employee in question from entering the workplace until the contagious period is over.