We had a mystery poltergeist when we first purchased our current camper.
I know for a FACT when returning from the campground back home, and parking in our driveway, blocking the jacks, and plugging in, the water pumps switch was turned off as the fresh water tank was drained on the trip home.
Alas ... poltergeist....
This repeated over and over and over again..... two or three days later I'd go out to the camper and the switch was on and the water pump running.
I'd flip it back off, and next day it was back on. Then it would go for a while and nothing happened. The it would do it again, very erratic, no pattern, couldn't figure it out.
We live in the country, we do have neighbors on the next property beside us, no fences, good neighbors, so I couldn't imagine anyone nearby us pulling a stunt like this on us.
After lots of frustration, I decided to double switch the water pump. I put a secondary switch under the bed, and simply spliced into one of the power lines feeding the pump. If either switch was off, the pump would not run. Both had to be on.
So, when returning home, I'd flip both switches off ... and it NEVER happened again!
I think it confused the poltergeist. To this day, I still do not know what caused it to happen.
I have no clue how long that pump ran with no water, but I imagine sometimes it was as long as 2 or 3 days. The old pump always worked just fine. Last year I did replace it, but not for this reason, like it burned out or anything.
Yes, they can run dry and not get hurt.