Previous apartment complex says we owe it money

by Jade
(albuquerque nm us)

So a few weeks ago my family and I were looking for a new apartment, we found one but later in the weeks they called to inform us that we had been denied because a previous aparment complex is stating that we owe them $4000 dollars 3 years later. We were never late on our payments but they are stating that we owe that in damages and for having to cancel our lease less then a month early because I had lost my job. We did not leave $4000 worth of damges they very slyly did our walk thru after we moved out without our presence, and stated that we left the place trashed. We have rented many other times and have had no issues but because we put in our notice where we are now they have our place to be rented out and we now have no place to go.