If your electricity is generated by natural gas, then a gas supply disruption will shut down gas AND oil furnaces.
If you lose power, it doesn’t matter what furnace fuel you use (for electric-controlled furnaces, of course). You’ll need a generator to run it.
If you have oil, propane or coal, loss of NG pressure doesn’t render your furnace useless. (That NG furnace is useless without NG flow, regardless.)
With propane, though, you can have non-electric, catalytic, oxygen-monitoring indoor heaters for emergency heat.
Most natural gas power plants are only online during the summer when natural gas demand and prices are lower.