I am not aware of any setting that forces a tech assignment to close. I would be interested to hear of that as well.
I set up an auto action that reopens any ticket that is closed without an assigned tech. It fired off a lot when first implemented but has trained people to make the tech assignment prior to closing. It does not fire off very often any more.
You can find the setting in Setup>Techs>tech groups>tech group levels>Auto-Assign Tickets To
Set this from none to any other option to avoid this going forward. I really like the idea of an action too, apap mentioned.
I have an action rule set up that changes the ticket status back to Open if one of my level 1 techs tries to close it when the Tech field is blank. It's quite annoying & so quite effective!