To put it succinctly, Sulla was a murderous autocrat who ruled Rome while it was still a republic. Despite the enemies he made during his career, it seems clear his death was not caused by an assassin. One forum poster asked how Sulla died. Forum poster dtn620 attempts to answer:

  According to Scullard's book, From the Gracchi to Nero, Sulla became a private citizen in 79 after he was no longer consul and resigned the dictatorship and went to live in his country estate....he died a year later at age 60 but Scullard doesn't identify how exactly he died, which leads me to believe he died naturally.

See the forum discussion for further information: Death of Sulla


Passage from Plutarch on the end of Sulla:

Notwithstanding this marriage, he kept company with actresses, musicians, and dancers, drinking with them on couches night and day. His chief favorites were Roscius the comedian, Sorex the arch mime, and Metrobius the player, for whom, though past his prime, he still professed a passionate fondness. By these courses he encouraged a disease which had begun from some unimportant cause; and for a long time he failed to observe that his bowels were ulcerated, till at length the corrupted flesh broke out into lice. Many, were employed day and night in destroying them, but the work so multiplied under their hands, that not only his clothes, baths, basins, but his very meat was polluted with that flux and contagion, they came swarming out in such numbers. He went frequently by day into the bath to scour and cleanse his body, but all in vain; the evil generated too rapidly and too abundantly for any ablutions to overcome it. There died of this disease, amongst those of the most ancient times, Acastus, the son of Pelias; of later date, Alcman the poet, Pherecydes the theologian, Callisthenes the Olynthian, in the time of his imprisonment, as also Mucius the lawyer; and if we may mention ignoble, but notorious names, Eunus the fugitive, who stirred up the slaves of Sicily to rebel against their masters, after he was brought captive to Rome, died of this creeping sickness.