This is the basic idea. It may not work. We really want a FET that will stay on reliably down to 0.9 or 0.8V. I am not sure if there is anything available that will do that. I suspect that this will work OK most of the time, but if you make a lot of units, or if you try to operate in cooler temperatures, it may cut off too early, effectively shortening battery life.
Note that the NMOS FET has its source connected to the battery negative terminal, and its gate connected to the positive terminal. As long as the battery voltage is high enough, the FET will be on, and current will flow through it freely. At some point as the battery discharges, the FET will turn off, and at that point, it will stop discharging.
You would still be able to charge it, as current will flow from source to drain through the FET's body diode until the cell voltage recovers enough to turn the FET on again. In theory.
simulate this circuit – Schematic created using CircuitLab