Is it permissible to take the basic structure of the database from the client without informing him, in order to make the necessary modifications to the program, given the client's refusal to hand it over?

If the modification in the database is a right exclusively yours, then there is no impediment to accessing it through appropriate means, as long as no one is harmed; this is based on the Prophet’s (peace be upon him) saying: "There shall be no harm or reciprocating harm." The consent of the one who withholds a right is not a condition for accessing it.