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Legal Issues!
Minimum 200 words response with reference. Need by 1/20/17
What can an employer do if the person stops working and goes to another company doing the same work, can the previous company stop the person from working there?
Are employers responsible for independent contractor's actions while they are working?
Limiting and employee's ability to work for a competitor is known as a "non-compete." A Google search shows that the enforceability of non-compete rules is generally very limited and varies for state to state (legal jurisdiction).
See: http://www.hrexaminer.com/is-your-non-compete-agreement-enforceable/
http://www.beckreedriden.com/50-state-noncompete-chart/
As to independent contractors' actions, you first need a legal definition of who is an independent contractor. See: http://www.imacorp.com/sites/default/files/IMA_Whitepaper_IndepContractExposuresGuidelines_2015.pdf
As to liability, it depends on the case. If they are hurt on your site? or are they acting independently? See:
http://theemplawyerologist.com/2016/01/21/can-you-be-liable-for-an-independent-contractors-injuries/
http://www.pashalaw.com/business-sued-independent-contractor-did/
Also note that Uber and other companies are currently having issues defining who is and is not an independent contractor. (http://uberlawsuit.com/ )
p.s. if something is not clear, or even if it is, Always consult a lawyer.