Alternate Fate??

You just need to do some side quest or talk to people or use some items. It depends on character in question. For example to change your familiar fate you need to talk to a some guy in lab, where you got a dollhouse, find blue and red resonator(on the way to Eliza's hometown) and talk to Carnos before doing castle mission. This way you can save your familiar from dying.
P.S.
sorry for my bad english, i am russian :)

So are you curious as to what is required to change someone's fate? Because if you are, it sounds like you've got it about right. More or less, changing someone's fate involves getting in the way of what would originally cause them to die. Some require you to save them in battle when they would originally die. (IE Mortis in Klahsdal) Some require you to use items at appropriate times, (Alfonse in Fort Baltrick), while others require you to complete their personal side quests that will eventually lead to their happier lives. (Elena, Magnus, Muntzer, etc.) It all just depends on the character, but you are more or less hitting the mark.