Transformer and a relay in series - but function like in parallel, but not exactly
There is a couple of methods commonly used in your situation.

1) (not recommended) Use the protective Earth ground connection that should be present in your box instead of a Neutral connection.

Note that although this works quite well from a technical perspective, it won't pass UL or CSA certification (nor most other certifying authorities).  One reason is that if the Earth connection should become disconnected or broken, you are deliberately passing current down the Earth conductor, which would cause it to become live in the event of a disconnected Earth.

2) Do some fancy phase control during the ON state.

Stealing power while the switch is OFF (open) is easy - you treat the Switched conductor as if it were the Neutral.  That is: the load provides the continuity to the Neutral conductor.  You will have approximately the full AC mains voltage across the switch.

This is (usually) OK so long as you are stealing only a few mA. However, there are some loads that this won't work with - I'm thinking of the little Egg-shaped strobe lights that used to be in discos in decades past.  There may be other loads that aren't happy with this as well.

Stealing power when the switch is ON (closed) is a little more difficult.  What you do is use a triac as the switching element and delay turning the triac on until the voltage across the triac is the desired supply voltage that you are trying to achieve.  A diode picks that voltage off and stores it in a bulk storage capacitor.  Then turn the triac ON.

Modern X10 light switches and some other smart light dimmers work this way.