Despite who you want to blame , a mentally healthy person does not kill themselves because they were bullied.
WHen this does happen, al adults involved can take some blame for not stepping in. The bullies parents should have recognized and either 1.) monitored or removed social media 2.) held the school accountable for any actions taken on school property. 3.) involve the bully's parents 4.) involve authority's. the list goes on.
And no a bully does not alway learn their behavior because of poor parenting. Are they at fault for the act of bullying? Yes. Are the at fault for a suicide..... No !!! Mentally stable people do not commit suicide and can't not be brought to that action by another person.