How to have a bad power supply fail safely?
Are you trying to make it burn/explode on purpose?  Some things to be careful about would be fire, smoke, electrical short to high current, live wall voltage.
Fire
Put it on a large concrete slab or something non-flammable.  Maybe build a platform out of concrete paver stones.  The adapter may burn but it won't catch other things on fire, e.g. your lab bench.
Explosion
Put it inside a Plexiglass box, possibly with holes to vent gas pressure, or metal mesh cage, sturdy enough to retain small pieces without exploding itself from the internal pressure.
Smoke
Put it under a vent hood, or vent the room well with a fan (preferably with smoke filter), or do it outside, because the smoke from burning components and plastic case will be unhealthy to breathe.
Electrical Short
A dead short on AC mains power can draw enough current to melt copper wiring and send droplets of molten metal flying in all directions.  You do not want to be staring into this without safety goggles on when it happens.  Stay far away and use a video camera to record what happens instead.  Be sure you can kill power to the adapter without having to touch it once you see problems occurring, for example by unplugging a long extension cable from the other end.  Also be sure your circuit breaker or fuse box is working, so you don't set your building on fire overloading the wiring in the walls.
Don't touch the damaged adapter until after disconnecting it from power and allowing it plenty of time to cool down and vent smoke and fumes.
Just because an AC adapter is poorly designed doesn't mean it will catch on fire as soon as you plug it in.  What are you planning to do to trigger a failure?