Current source improves linearity on collector BJT
I found circuits that use a constant current source instead of a
  resistor to improve linearity. How does this work?


All physical current sources are approximations of ideal constant current sources so there is no danger of the destroying the universe.  

We model physical current sources as ideal current sources with some finite (though large) parallel resistance.

In the AC small-signal model of a constant current source loaded CE amplifier, the small-signal collector current is through this parallel resistance.  This means that the small-signal gain can be quite large though at the expense of a very high output impedance. 

I don't think it's true that a current source collector load will improve linearity per se.  The fact that the circuit has high gain doesn't imply greater linearity for large signals.

However, the high open-loop voltage gain can be traded for linearity via negative feedback.