Overstaying a visa, regardless of duration, is a serious offence and is therefore subject to penalties. The possible penalties for overstaying a Schengen visa are (inversely ordered by severity):
- no penalty
Note that you can be subject to a combination of these. For example should you be deported you'll probably be recorded and banned too. Overall the applied penalties depend on a number of factors including the country in which you committed the offence and the individual immigration officer who deals with your case.
Your 1-Day Overstay
It is very difficult to predict which one will apply to a one day overstay. It'll probably depend on the immigration officers leniency and how well you can convince them that you didn't overstay intentionally. You can safely assume that if detected, the violation will be recorded and you're likely to be asked questions about it next time you apply for a Schengen visa.
To avoid overstaying you need to pass exit checks before 23:59:59 of the last visa validity day. You might want to try getting to the airport on that last visa validity day and see if you can make it past the checks on time.