Does turning off a classifier close the cases it already opened?

No. A case a classifier already opened stays open, because closing it would read as the regression having resolved itself when nothing actually changed except your settings.

Turning a classifier off suppresses it going forward: it stops writing new findings, stops paging anyone through alert rules, and its detail pages become unreachable while it’s off. What it already found stays visible in triage as history, and any case tied to it keeps its own state rather than getting silently marked resolved. Turn the classifier back on and its findings and cases pick up again where they left off, since nothing about the case’s own record was touched while it was off.

The distinction that matters: hiding a classifier changes who gets notified going forward, not what it already found.