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This is the maimed statue of the poor archangel on the roof of the “Cappella della Visitazione di Maria e di San Michele Arcangelo” (Chapel of the Visitation of the Virgin Mary and of Saint Michael Archangel).
Better known with the simpler name of “Cappellina dei Cassieri” (Cashiers' Chapel), it was bult in 1703 with the contribuition of the money changers of Livorno.
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An inscription was added in 1932 when the building was restored at the expense of Gino Cipriani, a civil engineer, who wanted to honor his wife recently passed away. It says: “Restaurata nel nome e nella memoria di Giuseppina Cipriani Ricci - Anno Domini 1932” (Restored in the name and memory of Giuseppina Cipriani Ricci - Anno Domini 1932).
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The dome was struck by a lighting in 2009, three days after I took these photos, and the cross had to be removed for safety reasons.
This is quite curious condsidering the original inscrpion in front of the chapel:
Sacellum Deiparae Visitationi
et Sancto Michaeli Archangelo dedicatum
Abiit in montana dilectione humilitate et gaudio
Rebelles fulminat gloria, zelo et justitia
I Cassieri di Livorno l'anno 1703
Chapel dedicated to the Visitation of the Mother of God
and to Saint Michael Archangel
(She) went into the hill country with love, humility and joy
(Saint Michael) fulminates the rebels with glory, justice and zeal
The money changers of Livorno in the year 1703
Thanks to my friend Silvestro for the translation from Latin.