The charging method for lipos is constant current, causing the cell voltage to rise, then constant voltage - holding the voltage (usually 4.2V for most cells) whilst the current draw drops then terminating charge once the current draw has fallen below a preset value, such as 10% of the full charging current.
Powering a circuit from the cell whilst its being charged could mean that the current draw never falls below that 10% so it will never finish charging. If the circuit draws more current than the charger provides, the cell will never charge.
A way around this is to provide a path for the charging circuit input to power the circuit, as well as charge the cell.
I've seen the term "Power path" used for Texas instrument and microchip products.At its most basic, the cell powers a circuit via a P-channel MOSFET, with its gate tied to ground so its on. The gate is also connected to the charger power input, so when someone plugs in power to charge the cell, it turns off the MOSFET, and instead powers the circuit via a diode form the charger input.
This effectively isolates the cell whilst its charging, and the circuit will only draw power from the charge input, via the diode, rather than the cell. See the attached image.
Note, the image uses a module with built in protection. If you dont' need that, then the cell just connects to the OUT+ and OUT- points.
There are some caveats here. The input is assumed to be 5V. This means that, when charging, it can only provide ~4.4 - 4.8V to the circuit, because of a voltage drop across the diode. If that circuit is a boost converter, it may (or may not) be too high for it.
If one uses a switching charger that takes, say, 12V input, to charge a 4.2V cell, then this system will provide ~11.4-11.8V to the circuit.