I work for the same company, but based in US now. I left China without cancelling the residence permit. I need a business visa to travel there, but now I am told that I need to cancel the permit first. Can it be done locally in Chinese Consulate or through an agency in US? What would be the process for cancelling the permit?
I have not faced this exactly, but I would expect the most normal way is that the company office in China should to go back to the local PSB where they got the permit.
There is a process for revoking it.
They may be reluctant because it may be more expensive and complex with you (or at least your passport) not there.
But I believe it's always that local issuing authority that is expected to do it.
You might push the company to be sure to file the permit cancellation request as showing you did nothing wrong - you mutually agreed to end early.
Not conducting a proper exit procedure when leaving China can be rather trouble some, but there are agents who can try and help you sort the situation out and file the right papers etc to cancel your residency and ensure you have the proper leave letter etc from your former company which is absolutely critical.
However you must note that even if you complete the exit procedure you might still be denied a new business/tourist visa because of not previously following the rules.
Normally a good visa agent can organize this but as always in China the visa approval process is somewhat person dependent and not always as straightforward as one would wish for.