A Finite Element calculation is driven by out-of-balance forces in the model. These out-of-balance forces can be caused by a change in load/stresses Δσ or a change in displacements and strains Δε, and then uses the (simplified here) relationship:
Δσ = E * Δε.
That means that the calculation itself does not see an out of balance when you change the stiffness alone: there will be no change in stresses (Δσ = 0), hence no change in strains (Δε = 0), and vice versa.
If we would only change the stiffness E, but no change in σ or ε, then we will see:
0 = E * 0
Note that the Finite Element calculation uses increments to calculate the changes. So it is not the total that is used to calculate, but it looks at the differences, and builds up the displacements.

See also the Scientific Manual, e.g. chapter 2 and Appendix A.

Strength reduction
A change of strength, and particularly a reduction of strength, may on the other hand lead to displacements. When lowering the strength of the soil, the program will check if stress points do not violate the failure criterion. If it does, then this stress point is corrected by changing the stress in this stress point to make sure the stress state in this stress point is valid. This will then  lead to an out of balance force, and additional strains are being generated. This is also the process that generates displacements in the phi/c reduction method used for safety calculations.

If, however, the strength reduction does not cause any stress point to violate the failure criterion, nothing will change in your model.