A very good question! First of all, this assumes that there is evidence suggesting that our universe has more than the 'critical density' so that re- collapse will occur. This is not a foregone conclusion given the present state of inventoring the contents of the universe. Nevertheless, what would happen if we did live in a 'closed' universe with re-collapse an inevitable prospect?
We know that the conditions attending the Big Bang were phenomenally smooth, or at least made that way by a brief period of inflation. We also are pretty convinced that since the Big Bang happened, many black holes of a variety of sizes from stellar ( few solar masses) to galaxy-sized ( few billion solar masses) have had enough time to form. In the far future, just before recollapse, although any remaining stars and gas will rapidly disintegrate into a hot, compressed plasma similar to the one our universe emerged from, all those black holes will also be present then too. This will make the re- collapse a very un-smooth affair. As these black holes accrete mass from the surrounding plasma, and collide and merge, they will fill the last few years of the end of the universe with a horrendous flux of gravitational radiation and irregularity in the distribution of matter.
This means that the initial Big Bang and the final 'Big Crunch' are not simply time-reversed images of each other, but that the conditions badly violate time symmetry. The Second Law of Thermodynamics wins out. It remains to be seen whether all of that 'irregularity' in the end-state can get smoothed out so that the Big Crunch proceeds to its final conclusion; an end-state smaller than an atom, and similar in many respects to what the original Big Bang was like.
One prospect is that under these conditions, the 'scalar field' that may have jump-started inflation will again rear its head and cause the universe to expand, thereby avoiding the universe getting snuffed out of existence. Once born, we do not know if the Laws of Physics at high energy are favorable to the universe becoming a self-propagating, self-stimulating phenomenon or not.