Here is a patent for deceleration fuel cutoff submitted by Honda in the early 1980's:
براءة الاختراع US4434769 - Deceleration fuel cut device for internal combustion engines - براءات اختراع Google
I was also able to find a deceleration fuel cutoff patent from the early 1960's. In both documents the terminology indicates total fuel supply cutoff, not partial.
The main goal of deceleration fuel cutoff is to reduce emissions and damage to the engine. When you don't cut off fuel during deceleration hydrocarbon emissions increase due to more fuel escaping the cylinder. This fuel can heat up the catalytic converter, and cause backfiring.
DFCO is a condition that has to have specific conditions met. If you read the Honda patent, the MAP and RPM are taken into consideration. If fuel is cut off at to low of an RPM the engine can stall.
If you read about the Honda IMA system it mentions how the valves actually rest and seal off the cylinder during DFCO, allowing for less pumping losses (less engine breaking) so that the regenerative braking is soaking up more energy, rather than being wasted by the resistance from the engine.
Honda Worldwide | CIVIC Hybrid
It's pretty clear from the sources I posted that fuel is cut off 100% during DFCO.