Narcissus, daffodil, freesia, snowdrop, snowflake, grape hyacinth, various iris and most other early spring blooming bulbs and bulb like plants should be perennials. We plant them with the hope that the will survive after bloom to bloom for another season, and perhaps for many seasons. Some should multiply to provide more bloom over the years. Bloom is just part of their annual cycle.
Lily, crocus, hyacinth, tulip, anemone and ranunculus are not nearly as likely to bloom more than one year for a variety of reasons. Some prefer more chill in winter. Some dislike the long and dry summers. Some survive as perennials, but do not bloom again. However, in some special situations, they also can bloom annually. After spring bulbs, there will be a different set of summer bulbs.
So, what happens after bloom? After exhausting much of their stored resources on production of bloom and foliage, bulbs try to recover and regenerate resources for the following season. Most work to replace their exhausted bulbs with comparable new bulbs. They need foliage to do this, but eventually shed their foliage as their new bulbs go dormant for the following autumn and winter.
Of course, they all do this at different rates. Some smaller bulbs are surprisingly efficient, and shed their foliage as soon as the weather gets warm later in spring. It is amazing that they can store up so much in such a minimal time. Other bulbs shed slowly, as their deteriorating foliage lingers for a few weeks into summer. Foliage of summer bulbs that bloom later is likely to linger until frost.
Because it is essential to the regenerative process, deteriorating foliage can not be cut back prematurely. It is not always easy to hide either. In mixed plantings, it might be obscured by ground cover or other plants. Alternatively, warm season annuals can be planted over the area. Some of us braid daffodil leaves, but others believe that braids draw attention to the deteriorating foliage.
Those of us who still dig and store and perhaps chill marginal bulbs, must wait for complete dormancy.