Mafia 88. Corruption

Did I understand correctly that if the first rat is deprived of its special ability, both rats lose the ability to use it?

No, only one. You can only deprive the one that is using the ability. The second one doesn't have the ability as long as the first one is alive, so you can't deprive it of something it doesn't have.

I also thought so until I decided to reread the rules again.

The quote refers to the principle of operation, not the blacksmith's special ability. He deprives the ability to kill. He does not deprive the ability to infect.