When winter kills the main meristem, it looks like it has rotted. If the crown is still firm at the sides and only the top looks rotten it can still survive. If the whole crown has turned to mush rather than just the top then yes, it's a goner.
As for the heaving, Elena, do you plant them with the roots more horizontal or vertical? In other words do you do the AHS recommended method of making a mound in the hole you've dug and arranging the roots sideways over it before backfilling like this:
http://www.daylilies.org/AHSFA...
