Is it possible to make current flow through a transistor from the emitter to the collector without supplying voltage to the base?
The NPN transistor in reverse direction can be viewed as Emitter-base Zener diode with the breakdown voltage larger than 5V plus "ordinary" PN diode between base and collector.   







simulate this circuit &ndash; Schematic created using CircuitLab

And the typical values for Veb is 

BC337-40

Veb=8.2V at I=5.5mA

BC549B

Veb=8.3V at I=5.5mA

BD139-16

Veb=8.5V at I=5.5mA

BC639

Vbe=7.7V at I=500uA

BC337

Veb=7.9V at  I=500uA

2SC945

Veb=8.1V at I=500uA

And the emitter-collector breakdown voltage (Vec) is: 

BC337-40

Vec=6.7V at I=5.5mA

BC549B

Vec=7.2V; I=5.5mA

BD139-16

Vec=6.7V; I=5.5mA

BC639

Vec=6.3V; I=500uA

BC337

Vec=6.4V; I=500uA

2SC945

Vec=7.5V; I=500uA

And the "equivalent" circuit is :







simulate this circuit

And what is more interesting is that the emitter-collector "equivalent" diode act as a "tunnel diode" hence the negative-resistance region in emitter-collector avalanche breakdown.   

Look at the exampel: 

http://www.cappels.org/dproj/simplest_LED_flasher/Simplest_LED_Flasher_Circuit.html

http://jlnlabs.online.fr/cnr/negosc.htm