rjenkinsgb, thank you for your reply. Yes, that is a good alternative. I think it doesn't solve the problem but I will get those and try them to analyze my point (2).
I am using a Li-Ion flat battery with a protection board. The problem is that Li-Ion batteries shouldn't be discharged below 3v to prevent damaging it. The TP4056 stop discharging at 2.4v; that is too low. For this reason, I am trying to cut-off discharge at 3v considering a Vth=-2.4v (because the parasite diode of the P-Mosfet consume 0.6v, so when this mosfet is ON, at the Source pin I will have (3v-0.6v) and at the Gate 0v, that means Vgs=-2.4, and that turn OFF the Mosfet, disconnecting the battery from the load. That's what I'm not really sure if it will happen).
However, it is a little confussing because it os recommended to discharge Li-Ion batteries up to 3v , but the TP4056, a Li-Ion controller, stop it at 2.4v. Maybe it is not as critical as I think.
Do you have any idea regarding the point (1)?
Thank you!