In general a unit completes its movement action unless the rule says otherwise. So for instance, entering a new location, placing smoke grenades (there's nothing there that says it overrides a general rule), loading [D6.4], unloading [D6.5], Recovery [A4.44] and sD. The one notable exception is DC placement, which explicitly says the unit must survive "unbroken and unpinned." [A23.3]
Clearance also explicitly says the activity is discontinued when the unit "is pinned, or is no longer Good Order." [B24.7]
So I would argue that Search completes before DFF in the absence of a rule.
JR