Under what circumstances does the F-16 and possibly similar fighters deploy leading edge slats?
Technically, F-16 and &quot;similar fighters&quot; have leading edge flaps (LEF) (or droop flaps), rather than slats. The difference is that they don't form a gap between themselves and the main surface when deflected. This makes them usable at high speeds, whereas slats are typically used for low-speed takeoff/landing.
For fighters, the most important use for them is to extend the range of usable angles of attack (AoA), which is important for manoeuvring as well as for takeoff/landing.
For F-16, @Mr R posted some details. I have some info for Soviet fighters of the same generation.
MiG-29
LEFs have two positions, up and down (20°). They are deployed:

When landing gear is down (including takeoff and landing).
Automatically in flight when AoA &gt; 9° and M &lt; 0.8 (Mach number).
On manual override by the pilot.

Su-27
LEF on Su-27 don't have fixed positions and constantly track AoA in flight. Maximum deflection 30°.
They are automatically deployed to 3/4 of travel when landing gear is down for takeoff or landing.
The pilot has a manual override (down-auto-up selector).
For both aircraft, if LEF fail, the allowed AoA is limited to 10°, which is roughly half the normal (depending on speed).