There seems to be a lot of investment in the whole idea of Rome among Romans, putting it very lightly. So if a slave were to turn on their master, let's say a senator or a prominent publican, by running to some authority to tell them such, what would happen? Let's say the crime is orchestrating an assassination of another Senator or maybe the Emperor himself, or it's something unmistakably treasonous in general. So would the safety and betterment if Rome be seen as more crucial than maintaining slave-master relations?
Now, they might not believe me, but if I could somehow prove it by knowing their plans and having knowledge of circumstances that wouldn't make sense without there being a conspiracy, what would happen? If I was a slave who wanted to try, who should/would I even run to to tell them? How could I expect to be rewarded, if at all?
Did Romans generally feel free to conspire in front of their slaves with little fear of consequences? Would they even accept evidence on another provided by a slave if it meant it could set a precedent of slaves informing on their masters?
Are there any examples of slaves doing this or of attempts to do this?
At best, you would probably be sold to another master.
The most infamous class of informers in the Roman world were delatores - men who accused prominent Romans of various crimes (usually disloyalty or treason), often in hope of gaining a portion of the condemned man's property as a reward. Delatores relied on accomplices to gather the information they needed to make an accusation. These accomplices, usually known as indices (spies), were often slaves in the household of the accused.
Since the delatores were notorious for their unscrupulous charges, many emperors made great show of refusing to hear their accusations. A few went so far as to publicly humiliate delatores and the slaves who assisted them. Finally, to discourage groundless treason trials, the emperor Septimius Severus ordered that the information of any slave who sought to inform on his master was to be ignored, and the slave himself was to be punished (Dig. 49.14.2.6). This pronouncement may have restated an older edict to the same effect.
Although it is unknown how slaves who attempted to inform on their masters were punished, a passage in Suetonius' Life of Titus (8.5) suggests that they were sold to other masters. A few exceptionally unfortunate would-be informers may have been condemned to the arena.
K. M. Coleman, "Informers on Parade." Studies in the History of Art 56 (1999): 230-245