i am payed my 5000 rmb penalty for over staying in china?can i get a new chinese visa?

After you pay 5000 RMB for fine, you will be issued a 10 days exit visa (with *) by local exit-entry administrative department, you have to leave China within 10 days, however, it will influence your future application because * on your visa shows that you have overstayed in China.

And what about a person that did overstay but has an invitation letter to go back for a few days by a large company