When you go to shut down Solus, you click the power icon, then click shutdown. Then, a confirmation dialog pops up with "Cancel" and "Shutdown" buttons.
For whatever reason, Solus shuts down Steam before you click that final shutdown button. I'm not sure what other software might be affected by this, I haven't found anything else. I've tested a number of other applications and everything else stays open like it should. Steam is the only program that exits.
I made a quick screen recording with various applications open. Sorry for giant resolution, I use 2560x1440. https://i.imgur.com/IN1bRlc.gifv