  We study equilibrium states of a drop between flexible sheets clamped on both
ends. Revisiting first the case of parallel sheets, we find multiple equilibria
which we classify in a parameter space. In solution branching diagrams we
identify hysteresis cycles and folds indicating abrupt transitions, yet not
necessarily leading to channel collapse. Between nonparallel sheets, a drop can
stay in equilibrium away from the ends even when the liquid is totally wetting,
which is impossible between nonparallel rigid plates. We also show that
nonparallel sheets can delay or prevent collapse in comparison to straight
channels, suggesting thus a mechanism that protects slender structures inside
micro-devices from damage by surface tension.
