Why does a beheaded saint have the halo above the stump? Many Christian martyrs have been beheaded, and they are often shown in art carrying their own severed heads. Sometimes, the halo appears not around the head, but where the head should be, as in the following French examples:



St Denis, on the facade of Notre Dame de Paris (nineteenth century restoration).




Martyrdom of St Denis, in the Pantheon (Paris), by Léon Bonnat. Here, there are two halos in different styles!




A beheaded bishop and martyr (possibly St Denis again) in the Petites Heures of Jean de Berry; flanked by St Stephen with his stone and St Lawrence with his griddle (Bibliothèque nationale de France, Département des Manuscrits, Latin 18014, f. 105r). I don't know who the saint is behind them, with the top of his head removed and carrying his own brain - St James the Less, maybe?


What is the rationale behind showing the halo above the stump, instead of around the head? I am looking for answers that can speak to the symbolic purpose of the halo, and of the common practice of showing saints carrying their own body parts - not an answer based solely on aesthetics.
According to Wikipedia, the halo was initially used for Jesus as a symbol of His Glory. Applied to the saints, it could be the outpouring of God's Glory, often talked about in the Bible, where the living water would flow from you, or His Light shine from you. 
If the position of the halo is usually from the Head of the body then I would make the assumption that the glory does not come from the physical body/head but from the soul/spiritual body/head.