Help with latches but can't figure out why after several checks

In an async process, all signs must be assigned in ALL branches. In your code, LED_out is only assigned in the closed and opened states - it must also be assigned in all of the other states.

The way to avoid this is assign all signals in an asynchronous process a default value before the case statement. This way, if it is not assigned a specific value in a branch, it will take the default assignment.

process(state)
begin
  output <= '0';  --default assignment
  case state is
    when state1 =>
      --do something
      --no assignment to output means it will be '0';
   when state2 => 
     output <= '1';   --overrides default assignment
  
  when state3 =>
    --no output assignment, output is '0' again
  end case;
end process;

This way latches are avoided.