@ckristiansen,

Technically, but the company that sponsors you will need your passport and work permit in order to cancel the visa, and since people don't tend to give these documents to companies when they leave it doesn't practically happen.

The thing to be careful about is that in order to change employers once you are on a Z-visa, you'll need a letter from your current sponsor confirming that you've finished working for them as part of the paperwork involved in transferring to another sponsor. And then there is something like a 30-day period after you get that letter where you can legally apply to renew/extend your visa in-country. Any later and they're supposed to make you leave the country (although it really depends on connections and who is processing the paperwork).

In short, the process of changing work visas is complex and usually not worth it. So for all practical purposes if you're on a work visa but have left your employer you're good for the duration of the visa but will have to leave the country to get a new one when it expires.