Earlier quoted context omitted.
any offline transaction under your floor limit can put you into unauthorised overdraft e.g. a train ticket purchase from a guard using a mobile terminal
I haven't lived in Europe for a while but it used to be common to issue online-only debit cards (VISA Electron, Maestro etc) for this reason, have these fallen out of fashion?
they were very easy to spot as they didn't have the raised digits (for the imprinting machine... old fashioned offline transaction)
now they're coming back again, but still not super common