My master has had it conveyed to me that I am to do manual labor and various servile tasks about his city house. I've acted docile to make my master think I'll be a cooperative house slave, but mostly to avoid being sent to a mine or out to a farm where I'll be worked to death. When my master brings me home, how wary is he of the threat I might pose to him? Will he lock me up until I've proven myself to be docile, or will it be assumed that I've surrendered my will to be free? Will he worry that I might bash his head in while he sleeps, or harm his family? Does he take precautions to keep me in check?
There's a bit of a (dangled) carrot and a (bloody and menacing) stick for dealing with house slaves.
Tacitus (Annales 14: 42-45) preserves the case where the ex-consul Pedanius Secundus was murdered by one of his slaves. Roman customs required that the entire household's slaves (some 400) had to be executed. There was debate in the senate about possibly sparing those who were innocent of the crime but it was quashed when C. Cassius pointed out this draconian custom ensured that slaves knew their survival lay in keeping their masters alive. The populace was not supportive of the mass executions and Nero had to line the streets that the slaves were marching to their execution with soldiers to ensure that the penalties were carried out.
The carrot was the possibility of manumission. One of my profs described it as a lottery that a slave could participate in for good behaviour. The reality was only a small percentage of slaves would receive their freedom (or the opportunity to buy their freedom). For the vast majority, it would remain a carrot dangled on a string before them. However as a household slave, you'd be in daily contact with your master which meant you might earn his favour which could lead to manumission.
An example would be Cicero's secretary Tiro who he freed in the latter's late 30's. On the other hand, there is the example of Seneca who had a 'favourite' slave yet was kept in servility even into their old age. Certainly many were freed but it seems that sometimes the impetus for manumission was financial. A slave with a trade could earn enough money to pay for their replacement. Then as a freedman, they'd still be dependent on their ex-master for contacts and capital and be bound by custom as a client. Plus the master no longer had to feed them.