Do nurses have continuity of care if they have a CNA?

I don't know of any "continuity of care" law. A CNA walking out would certainly put their job in jeopardy ...and possibly their certification.
A nurse needs to give report to an *accepting* nurse before leaving their patients. We can't just walk off into the sunset if there's a charge nurse on duty.

A CNA would likely lose his or her job if they walked off without giving report, possibly their certificate too. As nurses though, it would be patient abandonment to leave a shift without another nurse taking over.

If a nurse were to abandon her patients, she would be held accountable for that, especially if a poor patient outcome were to result from it, by being reported to the board of nursing. The charge nurse or house supervisor might be *responsible* for finding a replacement, but not held accountable for the abandonment itself. Now let's say a CNA up and leaves mid shift. The nurses for those patients would be responsible for giving report to the replacement CNA, but the CNA would be held accountable. That's my understanding at least based on similar situations happening at my hospital and our policy.