Adding voltage cutoff to a circuit?

In all the following a TLV431 1.25V reference is specified.
This requires < 100 uA minimum regulation current compared to about 500 uA for the 2.5V TL431.

When on the TLV431 on voltage is about equal to the reference voltage - NOT 0V.

TLV431 current is a battery load even when output is off. At about 100 uA this drains about 2.5 mAh/day.

Voltage sensing divider is also a battery load. This can be small.

Hysteresis is not used in any of the following circuits - except the one copied from internet. A whiff of hysteresis could be used to stop battery on/off cycling when load is removed. Ask if unclear how to do this.

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(1) Opamp based
P Channel FET high side switch.
TLV431 1.25 V reference.
R2/R3 divide Vmin to = 1.25V.

(2) N Channel FET, low side switch.
TLV431 1.25V reference.
FET Vth << Vmin

(3) P Channel FET, high side switch.
TLV431 = 1.25V reference.
FET Vth << (Vmin-1.25)V

(4) From web - similar to my N Channel low side circuit.
From This discussion page.

Here R6 adds hysteresis.

You could use a reset IC like the MAX809. This will output a low level when the input voltage is below the device's threshold. If the input voltage is higher than the threshold the output follows the input.

You can use this voltage to switch an N-channel MOSFET, like the FDC653N.
You'll have to use a high resistance voltage divider for the input voltage, since the highest threshold available is 4.9V.
The MAX809 has several manufacturers. I prefer the OnSemi because of its low ground current.