That's what "personal days" are for.

Vacation days are days that are long planned.

Sick days are last-minute days for when you are ill.

Personal days are last-minute days for when, say, a pipe breaks in your apartment and you have to spend the day dealing with the mess. Or any other non-medical reason you have to be a person and not an employee for a day.

Generally people don't have to use those last minute days often and I don't think that's what OP meant.

It seems like people just were abusing it.

I have often heard personal days are to be used if say, you can't get to work due to transportation issues or if your child is home from school. If they aren't to be used that way how do they differ from vacation days?

Generally people don't have to use those last minute days often and I don't think that's what OP meant.

It seems like people just were abusing it.

To be honest, if people are not told they need to give advanced notice for using their time off they often won't - especially when nobody else does.

Obviously, it's not always possible to give advanced notice (illness or other unforseen circumstances), so most employers require a brief explanation when advanced notice isn't possible - "Sick kid," "car trouble," "illness," etc.

These are normal policies, but they must be formal policies and communicated to employees.

If those policies are in place and you have people violating them - then it becomes an HR issue, with formal reprimanded, so a low level manager shouldn't have to complain about it.