background check

A friend of mine is looking for a job. She had a trouble with the current job. She took something home from a job, so she was disciplined by her boss and the record is in her personal file. The question is: If the new company/gov/univ offer the job to her, would they find out the discipline when they do background check? I told her it is a minor problem, they only check drug and crime record. But she is still worried. Any one who has such experiences can help?