Is it permissible to acquire some books that the administration will burn without its knowledge?

What you asked about has two scenarios: The first is if their distribution has been decided. In this case, it is not permissible to take anything from them except with the permission of the competent authorities.

The second is if their burning has been decided. The public library administration may do so if the books have reached a condition where they can no longer be utilized. You have the right to take from them without the administration's knowledge, as long as the library is public. However, it is preferable to ask for permission and advise on distributing them as long as there are those who would accept them.