About 2-3 times a semester, a student comes to me with this type of question. They have done their research, and know exactly what the syllabus states. They even point to the exact policy, and then ask if I can make an exception and do the exact opposite.
The answer I give to this question is always the same. “If I make an exception for you, I have to do give everyone an exception to make it fair. So why have that policy in the first place?” I get that things came up. It may have been a rough semester for the student. However, that doesn’t mean one student can get preferential treatment over the rest of the class. In my own experience, students try to argue their case even more, and get upset when I stick to the syllabus. If a policy is in the syllabus, you should expect it to be enforced.