Why doesn't Sodium (Na) form duplet?

The atomic number of Na is 11 (2, 8, 1). Na loses an electron to achieve octet stability but why can't it just accept an electron to complete duplet stability?

• Why, of course it can. The problem is, there are not enough free electrons for everyone. – Ivan Neretin Feb 9 '17 at 8:05
• @Ivan Neretin Would you elaborate "there are not enough free electrons for everyone. "? – Mockingbird Feb 9 '17 at 9:26
• I mean, all $\ce{Na}$ can't convert to $\ce{Na-}$. But I guess that's not what the question was about, anyway. – Ivan Neretin Feb 9 '17 at 9:34
• Possible duplicate of Is it possible to have a diatomic molecule of sodium in gaseous state? – bobthechemist Feb 9 '17 at 13:12
• @bobthechemist The questions are completely different even though they might have a similar answer. It is absolutely not the same asking "Why doesn't it accept an electron?" and "Does a dimer exist?" – Martin - マーチン Feb 9 '17 at 14:39

It turns out that $\ce{Na}$ and other alkali metals can actually be reduced to form alkalides, but those are exotic compounds. They are not particularly stable, and get oxidized with pretty much anything. It is much easier for $\ce{Na}$ to form a cation, thus achieving the stable octet, and call it a day.