[avalys]

Every multi-engine airliner is designed to be able to take off safely even if an engine fails at a critical moment. What might have happened in this case is that the mechanism of failure of one engine caused damaged or interfered with the operation of another engine (via smoke, debris, etc.), and taking off with two engines degraded is not part of the design criteria.

[pixl97]

I do think 'engine fails' and 'engine has left the building' are two different categories of problems. Even if the rear engine was working I'm going to assume this craft would have crashed, probably just farther down range.

[HPsquared]

Some engine failures can't be contained within the cowling, like turbine disc rupture. Probably something like this happened where fragments punctured the surrounding wing structure and/or fuel tanks.