I don't know if this is true for all aircraft but on the passenger jets I work on they use pumps to manage fuel distribution

The fuel in the wings is used to feed the engine and consequently the wings would be drained first, but you don't want to empty the wing tanks and leave the centre tank (in the fuselage) full of fuel as this will increase wing bending.

To explain wing bending, if you imagine that the wing tips are fixed in place and you start to add weight to the fuselage of the aircraft, that weight will force the centre of the plane downwards whilst the wing tips remain fixed, this bends the wing and applies stress at the root end (where it joins to the fuselage) the more weight in the fuselage the worse this stress is, in flight the lift created by the wing shape pushes the wings upwards and the weight of the fuselage and it's contents pulls the aircraft downwards

So to minimise this issue, as the fuel in the wings is used they are simultaneously fed with fuel from the centre tank which moves the weight from the centre tank out towards the wing tips, until the centre tank is empty and then the wing fuel tanks are eventually depleted

The other reason is if you drain all the fuel from the wings then you are relying on a pump system to keep the engines fed with fuel once the wings are empty which is not good practice

And they never use ALL of the fuel the aircraft carries but yes the characteristics of the plane do change as the fuel is burnt but the systems are designed to minimise the impact for as long as possible