If the bulbs are soft and brown, then they're dead, and it's better to remove them just in case a fungus takes hold and spreads to the rest of the plant. You were right about storing nutrients--a leafless bulb that's still green and firm should be left on the plant. If the rhizome (the horizontal part that holds all the pbulbs together) is firm and not soft, then you don't have to cut off any part of the rhizome.
I really hope yours makes it! It takes time and patience.
