Most employment is "hire and fire at will" and certainly a criminal conviction could easily be one of several issues resulting in termination or rescinding a job offer. Most job applications ask about a criminal records and often criminal background checks are run on prospective job candidates.
Please be advised that no attorney-client relationship is created by the discourse regarding your legal question. You should consult an attorney of your choosing to fully protect your rights.
An employer may typically deny employment based upon a conviction or other criminal records (charges etc.). HOWEVER, if the employer uses a criminal background report which is purchased from a consumer reporting agency (a private company that compiles your information from outside sources and then sells it to a third party) to make an employment decision, it must first, provide the job applicant or employee with a copy of the report and a copy of the summary of consumer rights. This summary tells the job applicant or employee how to contact the background company and dispute the information if it is wrong or misleading. This information must be provided a job applicant BEFORE a decision not to hire (or to fire if already hired) is made. Again, to allow the person time to discuss or correct the contents of the report. If this does not happen, then the employer may be liable for damages in a law suit.