Hi, Hyacinths die back naturally and go dormant after blooming. The foliage will eventually all turn brown and die. At that time, you can remove the dead foliage. If your plant was in a pot ( a gift plant) then toss it. It will not rebloom or come back. If you have this plant already growing in your garden, it should come back next year if you have a cold winter. Those that are forced to bloom in pots as gift plants, basically are done and not worth keeping.