Electronic – Current mirror: is there a name for this NPN-PNP pair, and how does it work

It's a multiple collector transistor, and in this application it's being used (as it often is in ICs) as a current mirror. The Vbe drops of transistors Q20 and Q21 and resistor R6 set the current through the upper collector of Q22, and this current is then mirrored back down into Q20 by the lower collector. It also sets the current through the long tail current source transistor Q11.

You don't need to add anything. The TIP125 already has fairly low-value resistors in there:

Note that the actual leakage current (2mA maximum at 25°C with zero base current- Iceo) is pretty loosely specified. I would expect it to be more like 200nA typically (10,000 times less than the maximum guaranteed).

To figure out if this is okay (rather than just eye-balling it like I did!), consider say 0.5V across R1 (not quite turning on), which would require a current of 63uA before it would begin to turn on the input transistor. Looking at the 2N3904 datasheet, the guaranteed maximum leakage from the 2N3904 is 50nA at 25°C. Rule of thumb is that this doubles every 10°C, but even so, even at 105°C we should have less than 13uA of leakage current, which is about 1/5 of the current required to begin worrying.