When one engine fails in a twin-turbojet aircraft, is there a weight imbalance?
Since your question is specifically on "jets".
We need not worry about the critical engine.

There is one thing to be noted in most of the commercial jets. The engines are placed close to the fuselage in order to reduce the moment arm - mean that should an engine fail, there is a reduced difference in forces,as compared to if an aircraft had engines on the wings tips.

The following are two vital things to be carried out during imbalance due to engine failure:

1) Effective rudder (and aileron) control:

The rudder (and aileron) is used to maintain directional control in flight, acting around the normal axis. An engine failure will yaw (and roll) an aircraft, making the rudder (and aileron) the best control to counteract this.

2)Fuel Balance procedure:

The following procedure is for a Boeing 737 :


Detailed schematic of a B737 Fuel System:



The procedures vary from one aircraft to another. And for a turbo prop aircraft it's a whole new thing involving "critical engine".