Handle_event/3 gets no params on unchecked box?

You can use a with the same name as the checkbox and set its value to whatever you want.

this is what it looks like in the core_components.ex from phoenix_live_view

  def input(%{type: "checkbox"} = assigns) do
    assigns = assign_new(assigns, :checked, fn -> input_equals?(assigns.value, "true") end)

    ~H"""
    <label phx-feedback-for={@name} class="flex items-center gap-4 text-sm leading-6 text-zinc-600">
      <input type="hidden" name={@name} value="false" />
      <input
        type="checkbox"
        id={@id || @name}
        name={@name}
        value="true"
        checked={@checked}
        class="rounded border-zinc-300 text-zinc-900 focus:ring-zinc-900"
        {@rest}
      />
      <%= @label %>
    </label>
    """
  end

Pardon me, but can use a what? Your sentence appears to be missing a word there!

The behaviour you see is how html is supposed to work. Unchecked checkboxes are ignored when gathering a forms data.

I‘d suggest using the form helpers of phoenix to build checkboxes. They automatically add an hidden input as well (before the checkbox), which uses the same name and has an „unchecked“ value. So when the checkbox is not checked you get the value of the hidden input – when the checkbox is checked you get the value of the checkbox, which overrides the hidden input value.

My bad, to mark it as code,

there was a
<input type="hidden" name={@name} value="false" />

like in the example below