A hypothetical situation, and a doubt

This won't happen, yet...

On takeoff, one of your engines sucks in a bird or simply fails, and
you're left with just one turbine. You declare emergency, etc. but in
returning for a landing, there occurs a situation during finals - you
somehow botch up the approach or some unexpected weather is encountered
- which in normal circumstances would've warranted a go-around. Since
you can't do that now with one engine, how would you salvage the
situation?

No "I'm good enough never to screw up approaches" for an answer, thanks


Regards,

Ramapriya