Remember that the purpose of a Little Free Library is to share books, so perhaps the person taking all the books doesn’t have any at home, or is distributing them to others in their apartment complex, school, or retirement community. Over the years we’ve heard from many stewards who’ve discovered that a book “thief” really wasn’t a thief at all.
But if someone is repeatedly clearing out your Library and you suspect foul play, considering stamping every book in your Library or writing in sharpie on the spines to reduce the resale value. Put up a sign explaining that your Little Library is a community resource for everyone to enjoy and that you and others notice when the Library is mistreated. One steward successfully got the police involved. You could even consider moving the Library to a more public location, like a coffee shop or a school, if you continue to have trouble.