The word pillaban is the imperfect form of pillar in the third person plural.
See the full pillar conjugation

pillar

Creo que no pillaban nada, pero algo les conmovía.
I think that they hadn't got it at all, but something had touched them.
Solía hacerlo a menudo... pero siempre me pillaban.
I used to run away a lot... but they always took me back.
Ellos simplemente pillaban cosas.
They just took stuff.
Sabía que si me pillaban entrando en la oficina de la Sra. French, no sería bueno.
I knew if I got caught breaking into Ms. French's office, it would not be good.
Los demás no pillaban nada.
Nobody else could catch one.
Las noches eran todavía más largas que los días (también para mí), y claro, como a pesar de esa circunstancia seguía fotografiando, algunas fotografías me pillaban de noche, como ésta.
The nights were still longer than the days (also for me), and of course, as in despite of this circumstance I carried on taking photographs, some of them catch me at night, like this one.
Así es como nos pillaban, pero nunca nos castigaron.
But nothing ever happened to us.
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