I must step in here as I have a big problem of FFF's description.
The point of a "VMC" training (and I think the earlier convoluted debate on VMC vs VMCA was pedantry in the lieu of practicality, but that is another debate) is to teach the student to recognize when the aircraft is approaching VMC and to learn how to effectively recover from this dangerous low speed regime.
It is entirely unnecessary and IMO quite dangerous, to actually slow to a speed where full rudder can no longer control the aircrafts direction. For many common light twin trainers this will result in a speed very close to stalling speed.
A much better way to demonstrate VMC is to, after the aircraft is stabilized with one engine zero thrusted, go to full power on the operating engine and then reduce airspeed while maintaining direction. When I feel the student had put in about 1/2 of total rudder travel I tell the student to apply no more rudder but continue decreasing airspeed. As the aircraft starts to yaw and roll into the dead engine I have the student reduce power on the operating engine and lower the nose to accelerate in order to regain control, which teaches both the recognition of VMC loss of control and to have
the student practice the recovery procedure.
Incidentally the closes I have ever come to be killed by a student was on a ME training flight in a PA34 Seneca. The exercise was a engine failure on a go around. We climbed to 4000 ft AGL and set up with gear down flaps full and landing red speed. I then told the student to go around and as he shoved the power up I pulled one throttle back. For some inexplicable reason the student then applied full back stick. Before I could react the aircraft stalled and snapped rolled. I tool over control with the aircraft inverted and 40 degrees nose down
. If I had not been an aerobatic instructor I probably would not have survived. I take single engine work at lower airspeeds very seriously....