We have heard that some customers have had problems removing broken toe sliders and tongues - this only applies to bindings that come with the "hinge" EST baseplates. Bindings such as Diode, Genesis, Cartel or Escapade.
Since there is a stud connecting the two parts of the baseplate there is not a lot of extra space for sliders and tongues. For that reason, it takes some sensitivity to remove the toe sliders or tongues.
Try using some pliers so that you have a better grip on the plastic and push the strap from top to bottom by wiggling it forward and backwards. With this technique, it can be removed within seconds.