What if a pirate buys a land claim. Will the UEE now be bound to protect the unlawful player?

UEE security will engage any criminals that they encounter, regardless of whether or not they own property. They'll also, however, act to protect the property of any private citizen, regardless of whether they are a criminal. If a property owner is a felon and in the vicinity when a UEE force arrives to deal with another player committing a crime upon their property, both the owner and the other party would be considered targets.