You are looking for a battery protection IC (which the TP4056 isn’t, incidentally). TI for example makes tons of them, with internal or external MOSFETs, with various cutoff voltage and current combinations available.
Bear in mind that these are intended as your last line of defense against undervoltage; you should still design your load to turn off below your design “empty”. For example, with a regular 3.7V Li-ion, nearly all the energy is used up by 3.5V. Pulling out the last few percent of energy down to the absolute cutoff of 3V stresses the battery a lot for very little yield. So while the protection IC is for 3V, you still want to design your load to shut itself off at 3.5V. (You can use the last 0.5V as a “reserve” to display a dead battery screen or flash an LED or something when someone tries to turn it on.) The exact values are given in the datasheet.
In a project of mine, I use a fuel gauge IC to monitor state of charge, and when the battery is empty (= 3.5V), the system shuts down and the MCU sends a command to the charger IC to disconnect the battery. But if you don’t have an MCU, use a comparator and a load MOSFET or something.