Bonus question: what about for slaves in other environments, who aren't personally serving wealthy Romans? If I'm a slave, say, on a large plantation or in the mines, what are the security arrangements like, and do I have a chance of escaping? Where to?
Edit: a commenter suggested specifiying where in Rome and in what period I'm asking about, so I'm going to say during Augustus's reign, after the end of the civil wars. But if you want to answer for any other period I'll take that as well.
Unsure if this is permitted, but may I add a follow up question?
Is there evidence to prove there were Railroad style groups that aided escaped slaves during this era?
I think you may have to provide some context as to the where and when. The Roman Republic/Empire covered vast areas and endured for centuries. It would make a huge difference, for example, whether this happened in the context of one of the Servile Wars (the third one, i.e. Spartacus's uprising being the most famous), in an area currently being ravaged by war, or in Rome itself during, say, more stable times, such as the Nerva-Antonine dynasty.