I had this happen by accident a few times and never ran into issues; I just gave them a valid card upon check-in (Marriott group). Changing cards happens frequently and I would honestly expect a hotel to contact me if they are trying to put a hold on a card and the bank declines ... simply cancelling the res is not cool. There could be other reasons the card declines (e.g. Amex or Chase or whoever get concerned about some std charges and block the card until they talked to you ... happened twice to me last year).