jewfab

I'm going to ask @Simon to comment on this one since he knows the internals better than me.   It sounds like you possibly have a damaged injector drive but that doesnt explain the "back feed".  Your inectors should not have power on the other side when you turn the key off so it sounds like there might still be a problem with the wiring too?
Anyhow, hold off until Simon gives his advice.

I think on the nissan the injectors are hot fed. So will have a permanent fed to them direct from the battery.
Generally when a drive is damaged it will short to ground but I would not then expect a back feed.
But I do think there is drive damage that will need to be repaired.