From a UK perspective, the element of training which is most strongly
stressed (once the student can fly the launch) is launch failures.

There are (roughly) 4 cases to train for:

1. Cable break/power failure immediately after rotation. The recovery
action here is to lower the nose to the normal gliding attitude, or a
fraction lower, and land without using airbrakes. This is the most
dangerous to teach, as fractionally overdoing the nose-lowering spears
you into the ground. I believe the BGA recommendation is that this is
now only demoed to students, though instructor training requires the
student instructor to fly the recovery.

2. Break soon after full climb is established (150-350 ft). What the
instructor is looking for here is a rapid push over into a
substantially nose-low attitude until approach speed is reached, then
reaising the nose to the normal approach attitude. At this point the
pilot must decide what to do, which from this height is completing the
landing (straight ahead) with appropriate use of airbrakes. The speed
of push over is important, to maintain a margin above the stall. Slow
reactions require further training until the push over becomes
automatic. Making the decision as to how to land only after approach
speed has been reached is also vital - teaching a spin from a
simulated cable break opens a lot of studetns' eyes!

3. High break (700 ft or so). Push over and then decision-making. Land
ahead is not an option here, so the student has to learn to fly an
abbreviated circuit.

4. Awkward height cable break - at a 3,000 ft strip like my own this
is around 500 ft. Too high to land ahead, too low for anything like a
proper circuit. Push over as before then decision making, which must
not be too long delayed or the options run out. A tight, abbreviated
circuit is required with an uncomfortably low final turn. If decision-
making is slow, or the circuit not flown precisely enough, further
training.

In addition to simulated cable breaks, where the instructor pulls the
bung, we also teach gradual power failures of the winch. Here the
student should be signalling for more power and, when it doesn't
arrive, deciding in good time to abandon the launch and land
appropriately (as above).

I don'tknow of a UK winch club where students are allowed to solo
before they can cope with all these, which means that any winch
failure producesa safe landing back on the airfield.