I want to know if Sivir's Boomerang Blade does damage on its way back to you if you die when you throw it? Sometimes you die but want to do as much damage in team fights as possible before you fall. With that in mind, does it finish its animation and do damage?
Yes, Sivir's Boomerang Blade will finish its animation and deal damage even if Sivir dies while it is traveling. This includes both the damage on the way out towards the target as well as the damage on the way back.
You can see this happen in this video:
For historical records, here are the relevant frames from that video:
If you focus your attention on the circled creep, you can see that in the second frame it takes damage from the Boomerang Blade after Sivir has died.