Why does the base-emitter voltage in NPN transistor become constant

The setup above shows the experiment that I have been working with. During the experiment, the current $$i_c$$ and the voltage $$V_{be}$$ were measured for increasing $$V_{in}$$. At some point, the current through the collector will be constant, due to the barrier in the forward-biased base-emitter region being lowered as much as possible by $$V_{in}$$, meaning that its maximum value follows Ohm’s law.

As we further increase $$V_{in}$$, we will find that $$V_{be}$$ will go towards a constant value. Why is that? Shouldn’t it increase too? I have great trouble understanding this last part.

I will appreciate any help!