When I grew them in Houston, they went to mush when temps droped into the 20s. Sadly, down there, they came back gangbusters from the roots, even on the other side of my slab-built-on house where I didn't want them.
A neighbor here (northeast of Knoxville) leaves her dahlias in the ground and has done so for decades with success- implying that even when our ground freezes, it doesn't freeze deeply so fleshy roots do survive.
I wish I could give you a precise answer instead of indirectly related answers.

Ann, are you saying they ran all the way under the entire length of your house and came up on the other side?

I'm in North Knoxville and my elephant ears came back strongly. I divided them this spring because someone told me they will die if you don't. The babies are now big and thriving. I put some along the edge of a line of bushes, in a place that got only filtered light & to my surprise they seem to like it. I thought elephant ears needed tons of sun, but these didn't. I have noticed they like water. I don't water much and the soil is poor, but they still seem to do well. The shoots do come up in unexpected and maybe unwanted places, but you can dig these up and move them quite easily. I love my elephant ears!

I live east of Knoxville and I never dig up my Elephant ears, 4:00's, Dahlia's or Canna's...they all come back every year....I do add extra soil once I cut them all down though...:))

They dont need sun....mine are growing in full shade.

I only tried them once last year in Knoxville,they turned to mush and did not come back.

I live in Loudon, SW of Knoxville, my elephant ears come back every year with gusto! I have one in damp shade that has huge leaves and one in the front yard with a lot of sun and not very damp - not quite so big but beautiful just the same. Give it a try - if they die, someone will have a root to share with you for sure.

My "Elephant Ears are 7 foot high and the leaves are very wide about 20 ears and you can see the baby ears coming up. Had a couple of flowers on them for the first time this year, very surprise. They are in a big pot. I bring the "Elephant Ears" in before the first frost hit them which is about the second week of October and put them in the basement near the block window, also I'm using a plant light for about 6 hours a night. About the last week in May when there is no frost, I'll bring them back out doors for five mouths. The EE are 4 years old and the pot weighs about 100lbs plus. They will grow indoors without any problems and I keep them watered every two weeks....

so i cut mine down to the ground when the turned brown, i live in mississippi about in the middle of mississippi it did however frost here, but i buried them deep, how soon will i know if the will pop back up and flusrish again. i do not know what zone i am in.