When does the victim get abducted in the quest? Does it happen when you accept the quest or when you get the objective to ask Companions for work? Does s/he get abducted when you join the Companions? I've been wondering this for a while.

I'm pretty sure it happens when you accept the quest.

http://www.uesp.net/wiki/Skyrim:Rescue_Mission

From my impression, at the same time the quest is added to your logbook, an NPC randomly selected from a pool of NPCs who all meet certain parameters (e.g. no unique voice acting, non-essential, etc.) is relocated to the area which you're supposed to raid.

That's why, even if you've killed Sinding during Hircine's quest, he can still be the potential captive.

I did some experimenting and after three reloads it was always Ennis getting captured. With another character it was that "Gray-Mane or Battle-Born" guy over and over again.

Idolaf, never had to save him tbh. Skyrim works in mysterious ways I guess