This made me curious, so I checked my Keysight MSOX3000T to see how it behaves.
When set to 1MOhm, when off, it actually disconnects input, and keeps it off (high impedance) until scope initializes.
Then it switches in input atten and drops to 1 MOhm.
But, if you enable 50 OHm, and switch off the scope, it also disconnects internal electronics, but it KEEPS 50 Ohm terminator switched in. Scope stays 50 Ohm terminated even when OFF. All the time. I guess they used bistable relay for 50 Ohm termination.
So if you keep scope at 1MOhm, it will completely disconnect inputs when off, but if you were working with 50 Ohm before switch off, input will stay at 50 Ohm even when scope is off.