The wire is the kill wire. This needs to be grounded to kill the engine - as it is, if you do ever get it started, you won't be able to switch it off!
Usually, this wire connects to the throttle lever assembly, and is grounded when the control is moved to the 'STOP' position, or it is connected to a flywheel brake assembly that kills the engine when the operator lets go the handle.
The start then dies problem indicates a carburettor overhaul is needed. Fuel supply problem
phil_saunders@bigfoot.com
Phil Saunders
June 2008