No, it's not possible to do it without current draw. You can do it with really, really low current draw though.
Ignoring MOSFET stages for the moment, I could design a system that could do this, with a power consumption of under 0.1 uA when in the low-voltage cutoff state.
I'd use a TPL5110 and an Attiny10 to do that.
Alternatively, if ~50 uA is OK (it really should be), then I'd just use the Attiny10 on watchdog timer, and save the cost of the TPL5110.
If I absolutely did not want to use the SLA to power that system (as an academic exercise), I'd use a separate CR2032 coin cell. That ought to last 3-5 years. Or if there's ambient light, a calculator solar cell and a supercapacitor would make it self-powered. I could design a system that could last overnight on just a few hours of ambient light during the day. Modern microcontrollers are a marvel!
The amount of power drawn by a reasonably designed system should be many orders of magnitude less than the self-discharge of the battery. So not worth worrying about unless it's very poorly designed for some reason.