Why don't such ions form if half-filled or full-filled configurations are considered stable?
As also pointed out in the comments, there is no such thing as absolute stability. One species is stable only with respect to another species.

You may have come across the fact - that half-filled configurations are "stable" - while studying ionization enthalpy/electron gain enthalpy, or the electronic configuration of $\ce{3d}$ elements. Pay careful attention: the half-filled configuration is "stable", but only with respect to the neighbouring configurations. That is to say, the $\ce{2p^3}$ configuration is much stable than $\ce{2p^4}$ or $\ce{2p^2}$. Yet, $\ce{2p^3}$ is still very less stable than $\ce{2p^6}$. This is why, in nature, nitrogen prefers to exist in diatomic molecules, so as to complete its octet.

Now for the fully-filled $\ce{3s^2}$ configuration (sodium anion, aka "sodide"): again, note that the sodium cation is way more stable than the sodium anion, as the former has a fully filled octet, while the latter doesn't. (Sodide has indeed been formed, but by using special techniques only. See Wikipedia).

Also see: Why are atoms with eight electrons in the outer shell extremely stable? and Why do atoms &quot;want&quot; to have a full outer shell?