To what approximate density does the collapsing core contract before halting due to the strong nuclear force?
$10^{14}$ grams per cubic centimeter
The final stages of core collapse involve the matter reaching unimaginable levels of compression. After the protons and electrons combine into neutrons, the core continues to shrink until it reaches a density comparable to that found inside an atomic nucleus. This extreme state is characterized by a density of roughly $10^{14}$ grams per cubic centimeter. At this phenomenal concentration, the fundamental strong nuclear force, which is strongly repulsive at very short ranges between nucleons (neutrons in this context), finally overcomes the crushing force of gravity. This strong repulsive pressure acts as a stiff core or surface, instantaneously halting the inward fall of the remaining stellar material and setting the stage for the rebound shock wave.

#Videos
A Detailed Breakdown of Core Collapse Supernovae - YouTube