Sounds like what you have are the species daylily H. Fulva Europa . These daylilies are stoleniferous (spread by underground rhizomes) and don't usually set any seeds and yes they will survive just about anything . I just dug up about 2 heaping 4 ft x 4 ft wagonfuls of Fulva roots and you should know that if you leave any and I do mean any of the orange roots behind 1/8th of an inch thick and larger they will grow back . So if you dig up make sure to be very thorough and remove any and all root pieces from the location before you plant anything else.

You don't mention what zone you are in but do say you are hoping for evergreens and depending on your zone , Evergreens may or may not provide you with greenery year round . .