If an employee fails to disclose prior criminal convictions, even though they were not asked at the time of hiring, are employers potentially liable for their possible subsequent bad acts to customers?

There are several reasons why employers may want to know what their
employees are doing. Employers may want to monitor employee telephone
conversations in the ordinary course of their business in order to
evaluate employee performance and customer service, or document business
transactions between employees and customers, or meet special security,
efficiency, or other needs. Employers may also want to monitor
employees’ email for what employers perceive to be sound business
reasons. The privacy line and what is and is not private when at work is
blurred.

Discuss the following questions:

• If an employee fails to disclose prior criminal convictions,
  even though they were not asked at the time of hiring, are employers
  potentially liable for their possible subsequent bad acts to customers?
• Can an employer fire an employee for posting negative comments about work on their Facebook account?