/johnny
There are two things going on here. 1) certifying the primary run-off election, and 2) resigning from office.
If McDaniel can get the run-off nullified and rerun, then Cochran can simply concede the primary and finish out his term with no thoughts of resigning. The state's run-off law is a cascading top-two if one declines to run, until there is only one left.
Cochran can still resign his seat, but the governor would only name his replacement until January.
If Cochran is declared the winner and then he resigns, he creates a vacancy in both the Senate and the upcoming election. The governor still appoints the replacement in the Senate until January, but the Democrat will run unopposed in November. State law only allows the candidate to drop out for non-political health or family reasons.
However, if Cochran resigns due to senility and not election illegalities, then the state GOP can appoint a replacement candidate.
-PJ