I think that I’m much more likely to get the drill to catch as it exits the material than any point during the main drilling, something to do with the material thinning, and the drill the screwing in to the remaining material. Therefore I often put a block of mdf or the offcut under the workpiece (but still in the vice), that’s also true for drilling thin sheet metal, but then I would prefer a hole-saw or punch depending on the hole size.
Edit: actually, the ‘worst’ catch I ever had was centre drilling a rod of ebonite (vulcanised rubber) for a pen blank; the drill’s heat softened the rubber, which caused more friction, more heat, etc and in a fraction of a second it had gone an additional couple of cm in to the blank, which the cooled and tightly held the bit. Took ages to separate the two.