You should try not to overstay your visa under any circumstance. If you do overstay the visa the consequences can be drastic. A few countries may let you just pay a fine at the border. However, this is a very rare occurrence and in other cases it is a lot more complicated. You can potentially be deported from the country or even arrested. If deportation does occur, it will have an impact on your future travels not only to that country (you may not be allowed in for up to 10 years) but to other countries as well.
Most of application forms have a question on them about deportation. And if the answer is yes your visa to any country may be rejected. The USA for instance won’t issue you with an ESTA (electronic visa) and you will have to apply for an actual tourist visa in person at the US embassy. That is a complicated and lengthy process and rejections are common.
So in short, do not overstay your visa.
If it looks like overstaying is inevitable due to serious circumstances, you will need to report it to the police or local immigration authority who may assist and issue a special permit or extend your visa.
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