I need a bit more context to come up with an explanation:
Cum in crypta, per quam transeundum erat, pueri nobiles ex Asia ad edendas in scaena operas evocati praepararentur, ut eos inspiceret hortareturque restitit, ac nisi princeps gregis algere se diceret, redire ac repraesentare spectaculum (2) voluit. Duplex dehinc fama est: alii tradunt [here begins indirect speech] adloquenti pueros a tergo Chaeream cervicem gladio caesim graviter percussisse praemissa voce: “Hoc age!” dehinc Cornelium Sabinum, alterum e coniuratis, tribunum ex adverso traiecisse pectus; alii Sabinum summota per conscios centuriones turba signum more militiae petisse et Gaio “Iovem” dante Chaeream exclamasse: “Accipe ratum!” (3) respicientique maxillam ictu discidisse [here ends indirect speech]. Iacentem contractisque membris clamitantem se vivere ceteri vulneribus triginta confecerunt; nam signum erat omnium: “Repete!”. Quidam etiam per obscaena ferrum adegerunt.
First Suetonius uses direct speech, voluit, to narrate what happened. He presents it as fact. Then he says, "from hereon, there are two different stories: some say that ..." (alii tradunt). He proceeds to give both versions in a.c.i., the second one introduced by another alii. When he continues with direct speech (confecerunt), we must assume that he is finished with the uncertain alternative stories and returns to a factual narration about which there is no doubt (modern historians have a lot to say about that, though).
The infinitive vivere is part of the confecerunt sentence and indirectly depends upon it: "they killed him lying down and...crying out that he was alive ( vivere )". So vivere depends on clamitantem, which in turn belongs to the object ("him when he was crying out") of confecerunt. You couldn't read vivere etc. as yet another a.c.i., for then the finite verb confecerunt would be left dangling.