I think it appears that they were not planted in well drained soil and probably overwatered last summer.
That's why they rotted over the winter.

An experienced iris grower told me that he barely buried his iris in the ground, leaving almost half of the rhizomes exposed. I have followed his advice since. And my Iris that were planted like that and were barely watered all summer have thrived and multiplied.

Maybe you can replant them before the summer is over and don't water them, they'll do better.
And definitely do not mulch them. If you dig them up and replant them in spring they won't bloom as well because they won't have enough time to establish.

Good luck.
:-)