Is offering private tutoring to students who ask for me by name outside the company considered "stealing students," or does it fall under "supply and demand," and does the ruling differ if the students have expressed their desire to leave the company should they be unable to study with me?

If the contract is for a fixed term, it is not permissible to leave it except with the company's consent. It is also not permissible to entice students to abandon their existing contracts with the company.

However, if the employment was legitimately terminated and the students have not yet entered into a contract with the company, it is permissible to offer them teaching positions, provided that their data registered with the company is not used. Instead, this should be done through personal acquaintance or public advertisement.