Aside from the five stages of grief: denial, anger, bargaining, depression and acceptance, I find that characters usually go down two paths after experiencing death or loss. 1) The character gains strength from it, using the death to push them towards resolving their conflicts or 2) The character is forever changed by it, never ending the same way they began and death becomes the reason they are who they are. Let's look at two examples.
Harry Potter by J.K. Rowling
Throughout the series Harry encounters death and the loss of family and friends: Cedric Diggory, Sirius Black, Dumbledore, and more. However, through these deaths Harry finds in himself the strength he needs to fight Voldemort. Through the loss of losing those he loved, he finds the courage he needs to do what has to be done and thereby defeating Voldemort once and for all.
Wintergirls by Laurie Halse Anderson
Lia grapples with the death of her friend, first allowing it to consume her, dragging her down, but when she finally falls she realizes that what she wants is to live. Cassie's death propels her to choose life and therefore she starts to take the steps she needs to heal. She starts to become a different person.