I think it is possible. If we don't take the time and put in the effort to be united with God while on earth, why would we suddenly change our tune after death and embrace that which we do not know? In other words, even a "christian" can spend their whole life fashioning a heart of clay. When this heart of clay comes into the warmth of God's love, it hardens.

Yes and no. That which we start in life is quickened in our death:


1Cr 15:36 [Thou] fool, that which thou sowest is not quickened, except it die:


1Cr 15:37 And that which thou sowest, thou sowest not that body that shall be, but bare grain, it may chance of wheat, or of some other [grain]:


1Cr 15:38 But God giveth it a body as it hath pleased him, and to every seed his own body.
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But woe to those that abandon the spirit they have been given:

Mat 24:12 And because iniquity shall abound, the love of many shall wax cold.
Mat 24:13 But he that shall endure unto the end, the same shall be saved.
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Mar 13:13 And ye shall be hated of all [men] for my name's sake: but he that shall endure unto the end, the same shall be saved.