Does this van have a sensor if the oil gets low enough it will just shut off?

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I was driving not even 10 minutes up the road to get some ice cream(pregnant cravings), it's late, midnight almost. & I've had this van for about 2 1/2 months. But don't drive it often. Just to doctors appointments. this is the first time anything like this had happened. We was driving & immediately not even three houses down from our house we hear this ticking sound. I just turned on the heater, & we know nothing about cars so I thought maybe that's what it was being I haven't used the heater at all. Well anyways, I finally get on the main strip, almost to my destination & my oil light pops on & my car immediately dies. Doesn't sputter or anything. Just dies. My husband starts it back up, & we decide to head to Walmart to get oil (obviously) & right before we made it there it dies out again & this time won't even start back up. The lights won't even come on. At this point I'm freaking out. It's late & I'm in a town I just moved too & don't even know who to call. This nice man tried to help us out, by jumping it & was gonna follow us home if we could start it. But it wouldn't even start. The lights came in while the power source was connected but wouldn't start. But once you disconnect it goes out again. He had some oil in his car the 5 quart tub. We put half of it in there & just let it sit over night. I'm about to go back up there & see if it will do anything. What could this possibly be? Does it maybe have a sensor? Thank you in advance, we know absolutely nothing about cars!