bookworm
I agree, by applying the correct amount of bank you regain balanced flight, I was just trying to keep it simple to answer the original question.
Yellow Sun
Interestingly, as bookworm says, with the correct amount of bank applied, the ball will be slightly off. It's just operating within the limitations of its design, ie, seeking the lowest point of the guage, which because of the bank, is no longer between the marks.
All the above is more relevant (but not strictly limited to) small prop twins. In a typical modern jet transport aircraft, once the engine failure is under control, then the aircraft is flown wings level, using rudder as appropriate. The result will be a small sideslip.