An Allitnil is an "Anti-Clone", designed to combat the ever-growing number of Lintillas spreading across the galaxy.
Since the Lintillas' cloning machine could never be shut off without committing murder, the only way to keep the Lintilla population down was to get the Lintillas themselves to voluntarily end their own existence.
An equal number of male clones were deployed, sent to seduce the Lintillas, after which the Allitnils would request to be married. A marriage license would be presented.
The document that was ostensibly a marriage license would be, in fact, a carefully drafted "Agreement to cease to be". The Lintillas (the clones) and Allitnils (the anti-clones) would cancel each other out, as would be expected based on their names.
Both the Lintillas and Allitnils were introduced in the Secondary Phase of the radio plays, and have not appeared in any other adaptation.