She can do this because anyone can do this to anyone, at any time. If the people they do this to are innocent of what they're charging them with, they are pronounced "not guilty" in court, and voila! the charges go away.
If you are pronounced not guilty in court, you might consider speaking to an attorney at that time about defamation and damages.
Background check company reports can show arrests, charges and convictions. These records and (some) court hearings are public records, accessible by anyone.
You should be able to seal or expunge any arrest that does not result in a charge, any charge that does not result in a conviction, and some convictions (after a period of time).
False accusations can result in charges but charges without sufficient evidence should not result in a conviction.
It appears you need an attorney in your area to help you with the current charge and to put a halt to your sister's harassment. I suggest you keep a good record of all that your sister is doing and saying, this in case a police complaint or a civil action must be pursued against her in the future.