Hypothetically, it is possible for a design like the STEN (Mk1 to 3) to discharge a round if it was dropped on the butt with the block forward. The probability is slim though as it would have to have enough impact for the block to be forced rearward enough to collect and fire the round, but not to much that the block engages on the sear. A STEN dropped from waist height doesn't impart any where near enough energy on the block to cause this.
There's also stories of STENs discharging whole magazines. The fact is that the STEN couldn't discharge a whole mag by accident, in fact it could only ever be possible to fire one round by accident. After the first round had been discharged, the block would travel rearward under full blowback, just like if the trigger had been intentialy depressed. This would mean the block would come to rest against the sear and it would be impossible for a further round to be discharged (Unless the gun or ammo was unserviceable).
If any of the STEN series were dropped with the block in the rear and rotated position, a serviceable gun should never accidentally discharge as again, the sear would prevent the block from moving forward.
The STEN MkV introduced a new 'Safetly cocking handle MkV' which could lock the block to the body when in the forward position, stopping the block moving rearwards if the gun received an impact. This new handle was retro fitted to many thousands of the Mk1 to 3 guns making a unmodified gun scarce these days.
I think the STEN received a unfair rep, yes it was a cheap mass produced weapon, but it was just what was needed at the time.