A few charts may help a little, starting with one similar to yours

The value of \$R_{_\text{C}}\$ doesn't impact the near-zero (left) side of the results. (It only affects where each line ends on the right side.)
The small negative value region for \$V_{_\text{BC}}\$ is the forward-biased BC junction area. The BC junction cannot be passively driven forward-biased more than the BE junction. So the collector cannot go beyond the emitter voltage. That's why the left side doesn't exceed about a diode drop below zero on the curves there.
But that's a poor curve for what you want to see, I think. Let's look at it against an applied voltage, \$V_1\$, where the effect of the resistor is made more visible:

Now, you can more easily see that the collector current does in fact go towards zero. But only when the applied voltage goes to zero, also. Since the base junction is being driven with a current source, it has no choice about its current. But the collector current is going to obviously go to zero when the applied voltage there also goes to zero.
The slope on the left side is exactly what's required for a \$200\:\Omega\$ resistor. The slope is about \$5\:\text{mhos}\$, which is what you'd expect for the collector resistor. And the current doesn't actually reach zero until and unless the applied collector voltage also reaches zero.
The active mode is everything to the right of the left-side slope. The slope is just showing you that once it enters saturation, then the collector acts like a voltage source fixed hard and close to the emitter voltage and that the collector current is then entirely determined by the collector load resistor and the applied voltage. (Which is what would happen if you just grounded the collector resistor.)
It's not terribly complicated. For a while, when the collector current allowed by the recombination current at the base isn't sufficient to cause a large voltage drop across the passive collector load, then the collector "floats" and tracks applied voltage less the collector resistor drop and the collector current tracks the base current by a ratio. But when the base current is sufficiently large and allows more current than can be supported through the collector resistor (the applied voltage minus the collector resistor voltage drop would, if allowed, cause the collector voltage to go below the emitter voltage), then the collector just "gets stuck" close to the emitter and stays there. Then the collector current is just a result of the applied voltage across the collector resistor and is no longer a function of the base current -- saturation.