Can I hand in the broken calligraphy competition works?

Of course.

It's just that the evaluation results may have an impact. If you have to pay it, you need to indicate it when you sign it. It is suggested to rewrite it to show the importance of activities or competitions.

In a word, whether you take part in a calligraphy competition or a calligraphy exam, the works you have written for a long time are the testimony of your calligraphy level. You must submit or hand in, don't give up. Even if you don't succeed, you will benefit from it.