I was diagnosing a start and die problem and after swapping out the g14 relay car seemed to run better. One of the things I did was run 12 volts directly to the coil. When I did this and turned the key off the car continued to run. I understand that the coil was getting power even when switched off, but wouldn't turning the key off kill power to DME and in turn kill injectors? I'm wondering if previous owner wired dme directly into battery instead of through ignition switch.

 

Not if it shares a power source with the coil (Which I think it does via the junction box on the firewall).