you can also do

# parent LiveView
def handle_info({:new_card, card_id}, socket) do
  send_update CardStackComponent, id: :card_stack, card_id: card_id
  {:noreply, socket}
end

#component
def update(%{card_id: card_id} = _assigns, socket) do
  card = get_card(card_id)

  socket =
    update(socket, :cards, fn cards ->
      [card | cards]     
    end)
  {:ok, socket}
end

you have to have in mind that update/2 is going to be called on each render. More info about this here

Is also worth mention that you may want to maintain the state either in the LiveView or the LiveComponent but not both, as is mentioned here

Actually it seems that you might pass to each new connection in connect in your user_socket this particular PID or name of the Agent and it should solve this case. You only need one Agent, so you can name it, eg.

Agent.start_link(your_func, name: :myagent)

and later get from it

Agent.get(:myagent, your_get_func)

Also you can consider to use Registry, which is from Elixir 1.4 in standard library.

This agent can be in lib and you can just add it in the <app_name>.ex file as a single worker and supervise it with dedicated Supervisor if needed.