Jacomo is the friar who converts Barabas's daughter Abigail into a nun. Twice. And that's his high point: later, he and Friar Bernadine both get caught up in one of Barabas's murder plots after they (really awkwardly and incompetently) confront him about his involvement in the recent deaths in Malta.
And that's not to mention his greed. Jacomo and Bernadine are from rival orders, and when Barabas pretends to want to convert they resort to really petty squabbling over whose order will get to receive him and, more importantly, his money. Jacomo is ultimately a pretty sleazy guy. He all but licks his lips over Barabas's wealth. And then, when Barabas tricks him into believing that he's murdered Bernadine, his first thought is how to escape punishment. He even claims that, since he's a "sacred person," Barabas can't touch him.
In the end, Jacomo's brilliant plan of, um, running away doesn't work. Barabas successfully frames him for Bernadine's murder before the Maltese court and Ithamore later attends his execution.
Even though Jacomo isn't actually responsible Bernadine's death, you're not exactly crying when you find out he's been executed.