Hebrews 3:12 Take heed, brethren, lest there be in any of you an evil heart of unbelief, in DEPARTING FROM THE LIVING GOD.
3:13 But exhort one another daily, while it is called today; LEST ANY OF YOU BE HARDENED, through the deceitfulness of sin.
3:14 For we are made partakers of Christ, IF we hold the beginning of our confidence stedfast unto the end;
Doctrinally, what can we reasonably glean or draw from the above verses? Well, in my fallible opinion and that's all I can offer (as well as everybody on this forum..Fallible opinions.), the above verses suggest that whoever the writer is referring to are "part of God", partakers of God, one with Him in Messiah. You can't depart from what you were never part of. They are warned to "take heed", they don't fall into unbelief, and depart from the living God they're obviously part of.
In the following verses, the writer goes on to say, that the brethren should exhort each other daily... (...this implies that they're in a position to do that and indeed, many of the believers in the 1st century, lived together, in closely knit communities. Some of them even held all of their possessions in common, as it states in Acts 2:42-47, hence they were in close proximity to each other, every day, sharing their lives with each other in such a way, that they could exhort each other daily. )...lest their hearts become hardened by the deceitfulness of sin. For (because) we are made partakers of Messiah if (provided that), we hold (maintain), our first love / the beginning of our confidence, till the end of our earthly lives.
Rev 2:4 Nevertheless I have somewhat against thee, because thou hast left thy first love.
Rev 2:5 Remember therefore from whence thou art fallen, and repent, and do the first works; or else I will come unto thee quickly, and will remove thy candlestick out of his place, except thou repent.
Rev 2:6 But this thou hast, that thou hatest the deeds of the Nicolaitans, which I also hate.
Rev 2:7 He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the tree of life, which is in the midst of the paradise of God.
Those that, hold the beginning of their confidence/their first love, and do not harden their hearts through the deceitfulness of sin, will not fall, losing their eternal inheritance. These are the overcomers, those that walk with Christ, zealously, consistently, till the very end of their earthly lives. One can reasonably assume from the above verses, that, the writer of Hebrews was directing his words, his warning, admonition, at the Hebrew believers/believing Jews of his day, perhaps of a particular community, like the one in Jerusalem.
The elect, those that are actually saved, are the overcomers, who maintain their first love/beginning of their confidence/zeal for Jesus Christ, till the very end.