There is no law that prohibits a company from hiring someone without a relieving order. Among PSU units, they have a policy protocol for this and hence it is enforceable. In the private sector, it is not enforceable by law.
In terms of the notice period, it's an agreement between you and the employee. The recruiting company need not bother, since most of the time, the hiring company wants the employee to join early. At most, you could initiate proceedings against the employee to recover the notice period pay.
There are many companies that don't bother about the new joiners' obligations to the previous employer. They are only concerned about their interest. It's of no use writing letters to the new company HR. They are not going to bother, since you do not have control over them.
It's better to get the employee to pay you the notice period pay if you want to penalize him and pursue the matter. In case he does not respond to your letter, you will have to evaluate the cost of legal recourse versus the amount of recovery.