If someone is on H1-B and wishes to change employers, they must seek another H1-B. You are correct that the employer is the petitioner, but a person must be assigned to the petition. The employer cannot have a "standing" H1-B for an applicant, and that applicant cannot work for any employer other than the original petitioner. I'm not in the Nile. Quite the contrary, I have hired over 5,000 people in the past five years.