Need help designing LiFePO4 BMS disconnect alarm
You can achieve a zero standby-current solution using a MOSFET to drive the beeper. 

Voltage from B- to P- is about 0 volts when operational and then changes under disconnect. With either polarity a MOSFET can be biased off when the input is a short circuit and turned on when a voltage exists. Exact details depends on what appears across the BMS when tripped, but whatever it is will "not be a problem".  

Powering the beeper from the main battery is possible but would introduce more uncertainties (eg blown internal fuse or link may remove all battery voltage. A separate battery makes the alarm far more fail safe. 

Powering the buzzer with eg a 9V Alkaline battery will give 5 to 10 years of standby battery life (zero current) and a 9V Alkaline primary battery 10 years +.

If you can report the voltage across the BMS when operating and when tripped it would help. It MAY prove useful to connect a small (high resistance) "load" from B+ to P- (so small a current as to not cause problems) but this is to be determined based on measurements.

Q1: What is the voltage across the BMS (P+ to P-) when operating?  

Q2: BMS voltage when tripped?

Q3: Do you want the alarm to sound when the LOAD is removed but the BMS is tripped.? 



Example circuit:

"Lamp" can be buzzer or other annunciator.
Vin is ~0V in normal operation and some positive voltage under alarm condition. As the whole unit "floats" a voltage that goes negative under alarm conditions relative to some reference can be connected "upside down".
If Vin is less than about 12V R2 may not be\ needed but is useful for safety purposes. When equipped RR2 R1 divide Vin down to a suitable value.
Zener Z1 clamps gate voltage to a suitable maximum value - say 12V is OK in most cases.
M1 can be one of many small N Channel MOSFETS.
D1-Q1 form an optocoupler providing isolated alarm notification. 

Quiescent current is essentially zero. 
If BAT1 is Alkaline a lifetime of 5-10 years is expected.
If BAT1 is Lithium primary a 10+ year lifetime is expected.







simulate this circuit &ndash; Schematic created using CircuitLab