So it's perfectly reasonable for the furnace to turn off when it is disconnected, because disconnection would be a very strong signal for an error state instead of regular intermittent network/service issues.
Certainly, the standard smart thermostat set up is that your ecobee is connected to the Internet, but controls the furnace using good old-fashioned signal wires
The overwhelmingly most common connection between a thermostat and furnace is a contact closure when calling for heat, with no ability to differentiate between “thermostat is present but not calling for heat” and “thermostat is not present” as both present as "these T-T contacts are not closed/shorted together".
While it is controllable via the cloud, even without wifi it continues to function.
You could in theory put one next to the furnace in your machine closet but that would be dumb and expensive
Fail "safe"...not Fail "keep running"
It is extraordinarily hard to design something that can withstand that pressure and still be fit for purpose. The item needs to be able to withstand pressures in excess of ~10k psi for -10c, with the pressure rising as temp decreases.
The standard solution for people that need to winterize a building that will not be heated is to drain as much water as possible from the lines, and then fill them with a liquid with a lower freezing point.