<div class="wrap">
  <div class="btn">Кнопка
  <div class="btn__subcontent">
    Бомжи и масло
  </div></div>
</div>

* {
  padding: 0;
  margin: 0;
  box-sizing: border-box;
  font-family: sans-serif;
}

.wrap {
  display: flex;
  width: 100%;
  height: 100vh;
  align-items: center;
  justify-content: center;
  align-items: center;
  justify-content: center;
}

.btn {
  position: relative;
  display: flex;
  width: 300px;
  height: 100px;
  background-color: red;

  align-items: center;
  justify-content: center;

  font-size: 32px;
  color: white;

  cursor: pointer;
}

.btn__subcontent {
  position: absolute;
  width: 100%;
  top: 100%;
  left: 0;
  display: flex;
  padding: 16px;
  background-color: green;

  align-items: center;
  justify-content: center;

  font-size: 32px;
  color: white;

  opacity: 0;
  pointer-events: none;

  transition: 2s; /* Тут ставим чтобы пропадало не сразу */
}

.btn:hover .btn__subcontent{
  animation: qwerty 2s forwards;
  /* forwards останавливает анимацию на последнем кадре */

  pointer-events: none;
}

@keyframes qwerty {
  0% {
    opacity: 0;
  }
  
  25% {
    opacity: 0;
  }

  100% {
    opacity: 1;
  }

}