Hi @NatalieCussell
If you want to avoid a situation where students are in the quiz forever because they never submit, you need to 'force' a close, for example via due date, available to, or quiz duration. You can still let them have multiple attempts, and you could capture their achievement over multiple attempts via Mastery Outcomes.
You are seeing 1 January midnight because somewhere in your configuration there is a 'hard stop' that forces the end of the attempt to be that date eg term end date, section end date, course end date etc.
This is a relatively trivial issue for formative assessment, much more important for summative