What would happen to a 777 if the pilot flew it up and up and up?

[Agschmid]

20. It's wiki but it seems scientifically accurate...

The absolute ceiling, also known as coffin corner, is the highest altitude at which an aircraft can sustain level flight, which means the altitude at which the thrust of the engines at full power is equal to the total drag at minimum drag speed. In other words, it is the altitude where maximum thrust available equals minimum thrust required, so the altitude where the maximum sustained (with no decreasing airspeed) rate of climb is zero. Most commercial jetliners have a service (or certificated) ceiling of about 42,000 feet (12,802 m)[citation needed] and some business jets about 51,000 feet (15,545 m).[2] While these aircraft's absolute ceiling is much higher than standard operational purposes, it is impossible to reach (because of the vertical speed asymptotically approaching zero) without afterburners or other devices temporarily increasing thrust. Flight at the absolute ceiling is also not economically advantageous due to the low indicated airspeed which can be sustained: although the true airspeed (TAS) at an altitude is typically greater than indicated airspeed (IAS), the difference is not enough to compensate for the fact that IAS at which minimum drag is achieved is usually very low, so a flight at an absolute ceiling altitude results in a low TAS as well, and hence in a high fuel burn rate per distance traveled. The absolute ceiling varies with the air temperature and, overall, the aircraft weight (usually calculated at MTOW).[1]