For such students, the first thing to do is keep calm. The world does not end with low score in board exam, and it definitely does not end with a bad rank in entrance exams. With the focus shifting to education in past few years, students will not find them short of options. There are multiple options available for students from the science stream apart from engineering, medical, and dental.
Other streams: Were you planning to go for engineering or medical only because your peers were doing it. If such is the case, now is the time to consider other streams and assess your inclination toward them.
Other courses: Engineering or medical is not the end. If you are interested in studying science, you can always opt for a B.Sc. degree. Nowadays, B.Sc. degree is not limited to just Physics, Chemistry, Botany and Zoology. Universities across India offer B.Sc. degree in both regular and Applied sciences. Go through the list of courses available and broaden your choice.
Private Universities/ Other Universities: There are numerous universities in India, including private universities, which accept students with low score in board exams and/or JEE Main/NEET. Research your options well.
The bottom line is a low score or a bad rank is not a big hurdle. If you widen your horizons, there are multiple options available. Do not feel miserable for performing badly in one exam as it does not determine your worth, instead focus on what should be your next course of action.