quit job, working visa must be cancelled?

Hi, I'm having the next situation: I quit my job and my company began with cancelling my residence permit. I want to know what the relation is between cancelling a residence permit and what effect it has on the working visa (Z). Does the working visa also have to be cancelled? My office suggest me to cancel the working visa and arrange a tourist visa. this will take me at least a week and will cost me extra money. Can i keep my working visa while my residence permit is cancelled? and if i cancel my working visa, how long am i able to stay in china for travelling?