Isa 45:4 was spoken concerning Cyrus for sure, but the word 'elect' in this verse is used in reference to Israel, for whose sake GOD is using Cyrus.
Yes, Israel is designated as being elect, and God used Cyrus to return them to their land, so the point is . . . what?
What was the purpose of the earthly election of the nation of Israel? Why did God choose them out of all the nations, under the Law? Why were they sanctified unto holiness, but they were not all promised salvation? Why, as in Amos 3:2, God promised to punish them for their iniquities?
What does any of this have to do with the BOC supposedly replacing the nation of Israel?
What in these verses, nullifies the concept of a remnant being saved amongst the sinful nation and demonstrating divine Election and saving grace unto everlasting life, as taught in Romans 11:1-7?
Reformers connect the name Israel with Isaac; the son of promise and with Abraham as being the father of all those gifted with faith. This is our definition of being in the New Covenant. One spiritual body of believers; Jews and Greeks; saved by the grace of God throughout all history.
All souls, so named "Israel," will stand justified in Christ on the last day. Romans 11:26-27
Concerning the gospel, national Israel proved to be an unfaithful enemy, but concerning the election a remnant has been saved by grace, as promised to Abraham and the fathers.