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...