V1 is the decision point. If a power unit goes before this point, you stop. If a power unit goes after this point, you continue.
Unless of course, the B777 was sat at the end of, say, a 20,000ft runway. Then the captain might decide that he's got enough room to stop in. (But then you don't get many of those!)
Here's what Wiki has got to say about V1:
V1 critical engine failure recognition speed. V1 is the minimum speed in the takeoff, following a failure of the critical engine at VEF, at which the pilot can continue the takeoff with only the remaining engines. Any problems after V1 are treated as inflight emergencies. In the case of a
balanced field takeoff, V1 is the maximum speed in the takeoff at which the pilot must take the first action (e.g., apply brakes, reduce thrust, deploy speed brakes) to stop the aircraft within the accelerate-stop distance and the minimum speed at which the takeoff can be continued and achieve the required height above the takeoff surface within the takeoff distance. In this context, V1 is the takeoff decision speed.