As long as your alternator is working properly to charge the battery and keep the engines electrical system supplied with power the car should not die or stop when the battery dies.
When the battery dies then your lights may go dim or your vehicle will not start back up after you shut it off and you'll need to have a jump start to get the car started again.
But as long as your alternator is working properly the car should continue to run without dying and if your car does die then your alternator is likely bad or something else is wrong with the car.
You can get your battery tested for free at Autozone or Oreilly and also see if your alternator is working properly to charge it.
You can unhook the battery while the car is running and if it dies then the alternator is not working properly and if the car stays running your alternator is usually okay.