Noobian:
The TP4056 module has a discharge cutoff function that stops the battery from providing power when it's charge is too low to prevent any damage to the battery.
Dont beleive you.
The output of the TP4056 module connects direct to the battery and the load is connected across the same connections as well.
As the load does not go through the TP4056 module even if the TP4056 module were to shut down, the battery is still connected to the load.