You have invented this third type purely out of your own imagination. Think about it! The elect are "chosen TO salvation THROUGH sanctification of the Spirit" (2 Thes. 2:13). Choice/election precedes salvation as cause precedes consequence "chosen TO salvation." Hence, election is to salvation and if the third category you speak of is "born again" then it is due to election "TO salvation." However, you have salvation occuring due to some other cause in addition to being "chosen" (elected). You have a category of BC that were not "chosen TO salvation" but obtained salvation outside and apart from being chosen by God "TO salvation." Hence, you have ANOTHER WAY "TO salvation" apart from being "CHOSEN to salvation." You have two different WAYS to be saved when the Bible only has ONE WAY. God's way is stated in this precise order (1) chosen from the beginning to salvation (2) through sanctification (3) AND belief of the truth. HOwever, your imagination demands another way that omits the first two (1 & 2) and yet arrives at (3) for some you call BAC.
Furthermore, note the words "THROUGH sanctification AND belief of the truth."
One cannot be "born again" apart from either and neither is possible unless one is first "chosen TO salvation" as "chosen to salvation" stands as the primary cause where as "throguh sanctification AND belief of the truth" TOGETHER are presented as SECONDARY causes of savlation and thus consequential causes to having first been "chosen TO salvation" as this choice occurred "before the world" (Eph. 1:4) but sanctification and belief of the truth occurs in the actual time between your birth and death. You did not believe the truth "before the world" began but you were "chosen TO salvation" or "chosen IN CHRIST" before world began as there is no salvation OUTSIDE of Christ at any time. This cause and consequence relationship should be obvious as "chosen" is placed PRIOR TO ("from the beginning") either "sanctification and beleif of the truth" and must be as the latter occur IN THE LIFE of the elect while the former occurs from the foundation of the world. Hence, it is not possible to reverse the order given neither is it logical.
Moreover, 'sanctification of the Spirit" merely means "SETTING APART BY THE SPIRIT" and that PRECEDES "belief of the truth" but continues until glorification when it is actually completed.
However, your imaginative doctrine demands that obtaining salvation occurs apart from being chosen TO salvation. Your imaginative doctrine demads one can be born again by "belief of the truth" without either being "chosen TO salvation THROUGH sanctification."
The reality is that you are confused and the precise point of your confusion is that you refuse to acknowledge that ALL who turn against Christ ("antichrists") regardless of their profession manifest they were never really BAC at all but they went out from us because they were not of us, for if they had been of us (BAC) they WOULD HAVE NO DOUBT CONTINUED WITH US."