That’s not accurate. While the aircraft shouldn’t be nearly hitting the end of the runway on takeoff it’s normal for larger jets to hit a point before takeoff where they couldn’t stop before the end of the runway.
Pilots call that point V1 during the takeoff roll, which means whatever happens you need to take off. If one of the engines blows up, you still take off. When V1 is called on takeoff standard procedure is to take your hands off the throttle controls since a ground abort is no longer available as an option.
The pre-takeoff briefing usually includes something like the captain saying if there are any problems after V1 we’ll take the problem into the air with us and troubleshoot from there.