How do droops help to avoid stalls?
Similar to a leading edge flap, fixed in the extended position with no gaps: The nose is lowered, so at high angles of attack the flow still has its stagnation point at the round nose where on an un-drooped nose it would had slipped below the nose section.



This reduces the suction peak near the nose of the upper surface pressure distribution and consequently makes recompression towards the trailing edge much easier. This helps to delay flow separation and to achieve higher angles of attack and lift. If an aircraft had a roll instability at high angle of attack, adding a drooped nose on the outer wing will cure it of misbehaving.

The downside is that now at low angles of attack a suction peak will form on the bottom side and might cause local flow separation. This increases the viscous drag just when this drag component dominates overall drag. Consequently, aircraft which had been modified with a drooped nose do not reach their old top speed anymore.