Both Monaldeschi and Burigozzo appear to mention their own death.

The probability is that their annals, as we have them, have been freely dealt with by transcribers or continuators adopting the historic 'I' after the decease of the titular authors.
Giovanni Villani relates how, having visited Rome on the occasion of the Jubilee, when 200,000 pilgrims crowded the streets of the Eternal City, he was moved in the depth of his soul by the spectacle of the ruins of the discrowned mistress of the world.[1] 'When I saw the great and ancient monuments of Rome, and read the histories and the great deeds of the Romans, written by Virgil, and by Sallust, and by Lucan, and by Livy, and by Valerius, and Orosius, and other masters of history, who related small as well as great things of the acts and doings of the Romans, I took style and manner from them, though, as a learner, I was not worthy of so vast a work.' Like our own Gibbon, musing upon the steps of Ara Celi, within sight of the Capitol, and within hearing of the monks at prayer, he felt the _genius loci_ stir him with a mixture of astonishment and pathos.

Then 'reflecting that our city of Florence, the daughter and the creature of Rome, was in the ascendant toward great achievements, while Rome was on the wane, I thought it seemly to relate in this new Chronicle all the doings and the origins of the town of Florence, as far as I could collect and discover them, and to continue the acts of the Florentines and the other notable things of the world in brief onwards so long as it shall be God's pleasure, hoping in whom by His grace I have done the work rather than by my poor knowledge; and therefore in the year 1300, when I returned from Rome, I began to compile this book, to the reverence of God and Saint John and the praise of this our city Florence.' The key-note is struck in these passages.
Admiration for the past mingles with prescience of the future.

The artist and the patriot awake together in Villani at the sight of Rome and the thought of Florence.
[1] Lib.viii.cap.

36.
The result of this visit to Rome in 1300 was the Chronicle which Giovanni Villani carried in twelve books down to the year 1346.