Can we saturate the BJT in emitter follower configuration by increasing base current? If yes, what happens in the process? How does increase in collector current decrease \$V_{CE}\$ when there is no resistor to drop voltage between source and collector ?
Similarly, how do you saturate an optocoupler in the same configuration? (TRCT5000 for example)
Can we saturate the BJT in emitter follower configuration by increasing base current?
You can if (assuming you are using an NPN BJT) you can pull the base voltage above the collector voltage. This is usually undesirable. If you did this in a emitter follower it would mean you are essentially just using the transistor b-e junction as a diode, and not achieving the impedance transformation that is typically desired from an emitter follower.
How does increase in collector current decrease VCE when there is no resistor to drop voltage between source and collector ?
If there is no resistor to drop the voltage, then the transistor won't saturate (until the base voltage is taken above the supply voltage).
how do you saturate an optocoupler in the same configuration?
You could do it by starving the collector of current, for example by connecting a resistor between the power supply and the collector.
The transistor base is driven by connecting it to a circuit which somehow generates a voltage between the base and the emitter. Diffusion and electric field inside the transistor (due the short distances) cause that most of the current generated by the base-emitter input voltage is caught by the collector and only a small base current occurs - assuming there's voltage Vce higher than the saturation limit. This phenomenon, where most of the current is caught by another terminal clashes with our everyday impression how electricity works, but that's caused only by the fact that generally wires and insulation layers are much thicker than the average length of thermal random movements of electrons.
The remainder of the current caused by Vbe i.e. the base current is a fraction of the collector current when there's enough Vce. The inverse of that fraction is called current gain. That easily is interpreted as "BJT is driven by base current". That's not wrong when we want to have a simple thinking model for our circuit design calculations. Current gain is much easier to remember and to use in math than the complex non-linear voltage-current- equations of PN-junctions. But essentially we must cause a voltage between the base and the emitter to drive the transistor.
Emitter follower amp circuit has a feedback, which reduces the voltage which actually drives the transistor. Vbe = Vin - Ve. As said by others you can beat the effect of the feedback and cause the transistor to saturate by connecting to the base higher voltage than Vcc. That limits how much the collector current can lift the emitter voltage Ve.
Emitter followers which have Vin > Vcc may have some usage, but as buffer amp it's not useful.
