Constant Current Source circuit improvisation
It's not going to be an accurate constant current source because the voltage-current slope of the BJT is not that great but if you can live with this then that's OK: -



Ideally, once outside the saturation region, the lines would be horizontal to the base line of Vce - horizontal means that no-matter how you change the resistance of the load (which obviously changes the voltage across it and Vce, the current would remain the same. As you can see, the lines are not horizontal but have a gentle upward slope and get progressively less-horizontal for higher base currents. Added to this your circuit won't control the base current as neatly as you think - current through the emitter will slightly reduce the base current. If you want a better constant current source try one of these: -