The emergency training we got on our radar course simulated an aircraft ewith engine failure.
We were taught to expect a reduced rate of turn, expect the crew to turn into the dead engine and aviod vectoring over built up areas if you're trying to get back to the runway.
But the list is not exhaustable and situations vary.
At the end of the day if the crew have experienced a problem an the controller passes instructions and information appropriately to the condition, it is still the commanders choice to take the advice.
I'm assuming that most of you out there would state quickly to the controllers if you wanted to turn the other way.