Connecting only emitter to collector-BJT
The voltage \$V_{CE}\$ applied has to drop across the two junctions: collector junction and emitter junction. Now the sign of the potential will be such that one junction will be forward biased and the other will be reverse biased. Since base terminal is open, same current has to flow through these junctions. So a small current having a magnitude in the order of reverse saturation current of the reverse biased junction will be flowing.

Because of the bias conditions prevailing, say forward biased emitter junction and reverse biased collector junction, electrons from emitter will be injected to base (npn transistor assumed). These electrons will be transported to collector and contribute to current. The holes injected from base to emitter also contribute to current. But the applied voltage will be dropping mostly in the collector (reverse biased) junction and hence the current will be very small.