How do I detect when the search is cleared?

onChangeText fires on every change to the search input. When the field is cleared — by the user, by the "X" clear button, or automatically when the list closes — onChangeText fires with "".

<Dropdown
  search
  data={data}
  labelField="label"
  valueField="value"
  onChangeText={(text) => {
    if (text === '') {
      // user cleared, or the dropdown closed
    } else {
      // user typed
    }
  }}
  onChange={(item) => setValue(item.value)}
/>

When does the search clear automatically?

The component clears searchText (and thus calls onChangeText('')) whenever the list closes, to avoid the search-input state leaking into the next open. If you want to persist the query across opens, capture it in parent state inside onChangeText and re-apply it after open via onFocus.