BJT with collector base or base emitter shorted
With Base connected to Collector the transistor is on the knee going into the saturation zone. Depending on knee voltage the current gain may be a bit lower than HFE at standard Collector voltage. 

With Base connected to Emitter the transistor is turned off unless the polarity is reversed, and then the Collector and Emitter swap roles. The current gain is very low in this mode but it still acts like the other case. 

If the Base is not connected to the Emitter then the B-E reverse bias breakdown voltage can be exploited. The problem with this mode is that it is outside the absolute maximum specification (so if it damages anything it's your fault). The actual breakdown voltage is not usually specified either, so it cannot be relied on.