Overstayed Work Visa.

Long story but I washed my passport so had to have it renewed, whilst it was being renewed my work Z ran out. So the government are saying I overstayed my Z. I've tried explaining the situation and I have got my government to send letters to the fact. At the moment there is nothing in my passport, no visa nothing, I want to leave. Can I go to the airport and leave, if yes what would be the actions taken. If no help, I'm running out of money and I have flights already booked to go back to my home country.
Any advice welcomed.