What happens if I overstayed and I want to leave the country? Is there a safe way of leaving?

How long have you overstayed? If you didn't overstay too long, you just need to pay the fine. Then you can leave. If you overstayed for a long time, for example, one year, you would be fined and detained. Then you might be deported. In the future, you may not be able to apply Chinese visa successfully for this overstaying record.

No matter how long you overstayed, you should turn yourself at local PSB first.