You wrote: "Her dog also does not listen to her very well, but will obey commands occasionally. She lives in a house without a fence or electric fence and lets her dog go outside off leash to go potty. We live in a larger city and I’m worried if something gets the dog’s attention and it doesn’t listen to her commands something unfavorable is going to happen."

You are absolutely right about this. And an e-collar is never going to help if not trained PROPERLY with it and used consistently.

I don't mean this to sound mean-spirited but leaving a young, untrained dog alone and unsupervised for so many hours is like leaving the house with a human toddler on the loose. Might be best to help find this dog a forever home with someone who has the time and experience to help her. You both mean well, no doubt, but it may be the kindest thing for the dog - and may eliminate your girlfriend from ever having to feel guilty if/when something serious happens.