Adam, as others have indicated, people usually continue sailing with some kind of autopilot/automatic steering while they sleep. If you are solo I suppose the best you could do is to have radar and/or AIS (https://en.wikipedia.org/wiki/Automa...ication_System
) with some kind of proximity alarm to sound and wake you if anything detected or broadcasting came within a certain radius of your vessel (or appeared to be within a certain margin of a collision course per AIS).
AIS seems like a particularly good concept because it broadcasts YOUR position and heading (if you have a unit that sends and receives) as well as that of pretty much all major ships. So it makes YOU more "visible" to the ships as well as the other way around.
Unfortunately this, like anything else, is not completely foolproof. There could be objects not big enough, reflective enough, or high enough off the water to be detected by radar and not on AIS but that could still do you damage. This would include completely sumberged things like a whale.
Some of these might be detectable by an awake watchstander, but at night still might be difficult to see until you were right on them, if they were low in the water and there were waves.
So I think doing ocean passages incurs a certain amount of unavoidable risk. You can minimize that by being a good and experienced sailor, having a really good boat (especially if it's made out of metal, lol), and equipped with all the awesome safety gizmos as mentioned, and you reduce that risk further if you can have someone continually standing watch, but you can't eliminate it entirely.
Also, as the other poster mentioned, you can't really anchor on ocean passages, the water is way too deep once you are significantly offshore. You could "heave to" to move very slowly at night but this would be pointless as you could still get run over by a ship while "hove to" so you might as well continue sailing towards your destination. Getting there sooner should decrease your "risk window" by simply decreasing the time you are out there.
But my impression is that aside from getting damaged in bad weather conditions or freak accidents like a whale strike, the risk in ocean passages gets much higher as you get closer to land. More boat and ship traffic, and there are actual land features you can run into and get beat to pieces by waves against.