It was specifically said that every student and teacher individually signed the contract, so unless that’s a lie this is probably not what will happen.
The paragraph that speaks about the deal contains the sentence:
But she was not trusted, and so there was invoked a curse. Some curses are easier to cast when they bind yourself and others alike; Slytherin’s Parselmouth curse is an example of such.
There’s no statement that only the people who signed are binded.
It was specifically said that every student and teacher individually signed the contract, so unless that’s a lie this is probably not what will happen.
The paragraph that speaks about the deal contains the sentence:
There’s no statement that only the people who signed are binded.