The condition for the British Lord to let them die willingly was for the British Lord to give their families freedom after their deaths.
For these people, they would still die sooner or later without an antidote, so it would be better for them to die and give their families a chance rather than to die just like this.
In fact, these people were different from the Armed Calvary Guards and the dead soldiers. They were Ezra’s confidants. When Ezra brought them here to take office, none of their