The longest government shutdown on record hasn’t derailed major SEC fraud cases against a sitting congressman, a former Theranos executive and a ring of Ukrainian hackers.

The Securities and Exchange Commission is actively pursuing a handful of high-profile enforcement cases, even as stays have been granted or requested in more than 20 others, according to a Bloomberg Law review of lawsuits brought since Jan. 1, 2018.

Commission lawyers can’t work on existing cases or launch new investigations during the shutdown unless they involve “emergency enforcement matters,” which include threats to property, according to an SEC plan released last month. The...