2-wire analog buffers
They work because the power to run the op-amp is coming from the courrent-source that's connected to the output. 

For correct operation the op-amp must allow the input voltage to touch the positive or negative supply rail, and the current source mus provide sufficient current. 

With this setup you are also constrained to using only single device packages.

Take for example the LM321 an inexpensive single op-amp derived from the earlier LM324 quad op-amp. This device allows the input voltage to go slightly below the negative supply, so it's a good candidate for first diagram.

In this setup the one of the output transistors is shorted C to E by the V- to Out connection and so does not not participate, but the other can source current from V+ to drive current into the current-sink.



with the output connected to the negative supply (ground symbol) the section shaded in red turns off and plays no part, but the rest of the op-amp continues to function, the voltage at point 'A' is 1.2V above the negative supply allowing the rest of the op-amp to function.