When the consistency flag is not used (ncpu= positive number or by setting CONST=2 on *CONTROL_PARALLEL), summation of quantities (results) occur in a different order between runs. This leads to some randomness in the round-off error. For a model with failure and element deletion as in your case, this randomness can lead to bifurcation in the solution. If in a given run, the failure strain is reached sooner for a given element, then this element will get deleted sooner, which in turns will increase the strain on the other remaining elements near the element that was deleted. For this reason, a given run may lead to more elements being deleted compared with another run, even though you are running on 1 CPU.
When the consistency flag is activated (ncpu= negative number or CONST=1 on *CONTROL_PARALLEL), the summation of quantities is done in a precise order so that the round-off error is the same between runs. This ensure nearly the same results between runs.
You will find more information about consistency in the LS-DYNA User Manual Vol I in remark 2 of the *CONTROL_PARALLEL keyword:
You can download the LS-DYNA user manuals here: