It becomes a white dwarf . According to quantum mechanics, it is impossible to put two electrons, two protons, or two neutrons at the same place at the same time. This is not as obvious as it sounds. After all, two light beams can be at the same place at the same time, or a light beam and a window. When you try to put many of these particles of the same type in the same region of space, their avoidance of each other produces a degeneracy pressure .
Degeneracy pressure is much higher for electrons than it is for protons or neutrons.
It is very hard to pack electrons into a small space. Answer - You have a lot of electrons, and degeneracy pressure preventing you from entering a wall is enormous. Degeneracy pressure can be extremely strong. Degeneracy pressure doesn't care about temperature. If I cool you off, it still isn't easy to push you into the wall.