Slats or LE Flaps Vs TE Flaps
Slats improve the low speed handling of an aerofoil by a large amount due to delayed separtion of boundary layer, increased lift generating surface etc. while TE or LE Flaps increase the camber/ total surface area and thereby the lift and drag.
This becomes critical in a swept wing planform which has LE Flaps near the wing tips where the BL separation is ahead due to the transverse flow across the wing.
If the Angle of attack and the speeds which are meant for slats extended are used when slats have failed- then the aircraft is very close/in the region of reverse command, where there could be a large rise in drag for a correspondingly reduced rise in lift. if this is not detected quickly by a pilot then it could lead to a descend because the lift equation of the aircraft is not matching up. Hence the need to critical monitor airspeed and attitude during take off/go around by BOTH pilots. Hence any failure either LE or TE could result in disaster. Its happened to me when my co pilot raised the flaps to 0 by mistake instead of flaps 15 during a single engine (raw) go around at minima of an ILS. Luckily managed to control it. thank god it was in the simulator (but during a test). However my stick shaker did come on momentarily.
The situations enumerated by other contributors have been when the slats have failed but one knew that he/she had no flaps. A crash may happen even if the flaps fail. So beware of drawing half conclusions.
Hope this helps.