Socket socket = listener.accept();
InputStream in = socket.getInputStream();
byte [] mybytearray  = new byte [FILE_SIZE];
                    int bytesRead = in.read(mybytearray, 0, mybytearray.length);
                    int current = bytesRead;

                    do {
                        bytesRead =
                                in.read(mybytearray, current, (mybytearray.length-current));
                        if(bytesRead >= 0) current += bytesRead;
                    } while(bytesRead > -1);
socket.close();

WHILE offset_ < Dbms_Lob.GetLength(bTemplate) LOOP
        Dbms_Lob.Read (bTemplate, chunk_size_, offset_, file_chunk_);
        b := utl_tcp.WRITE_RAW(CONN, utl_encode.base64_encode(file_chunk_));
        offset_ := offset_ + chunk_size_;
    END LOOP;
 UTL_TCP.FLUSH(CONN);

 Socket socket = listener.accept();
                ByteArrayOutputStream baos = new ByteArrayOutputStream();
                TeeInputStream tis = new TeeInputStream(socket.getInputStream(), baos);
                try {

                    byte [] mybytearray  = new byte [FILE_SIZE];

                    while((tis.read(mybytearray)) != -1) {
                    }

                    ByteArrayInputStream bais = new ByteArrayInputStream(baos.toByteArray());
                    XWPFDocument document = new XWPFDocument(bais);
                    PdfOptions options = PdfOptions.create();
                    ByteArrayOutputStream pdfout = new  ByteArrayOutputStream();
                    PdfConverter.getInstance().convert(document, pdfout, options);

                    System.out.println("Final");
                } finally {
                    socket.close();
                }

 Socket socket = listener.accept();
                ByteArrayOutputStream baos = new ByteArrayOutputStream();
                TeeInputStream tis = new TeeInputStream(socket.getInputStream(), baos);
                try {

                    byte [] mybytearray  = new byte [FILE_SIZE];

                    while((tis.read(mybytearray)) != -1) {
                    }

                    ByteArrayInputStream bais = new ByteArrayInputStream(baos.toByteArray());
                    XWPFDocument document = new XWPFDocument(bais);
                    PdfOptions options = PdfOptions.create();
                    ByteArrayOutputStream pdfout = new  ByteArrayOutputStream();
                    PdfConverter.getInstance().convert(document, pdfout, options);

                    System.out.println("Final");
                } finally {
                    socket.close();
                }

WHILE offset_ < Dbms_Lob.GetLength(bTemplate) LOOP
        Dbms_Lob.Read (bTemplate, chunk_size_, offset_, file_chunk_);
        b := utl_tcp.WRITE_RAW(CONN, utl_encode.base64_encode(file_chunk_));
        offset_ := offset_ + chunk_size_;
    END LOOP;
	
    --RETVAL := UTL_TCP.WRITE_LINE(CONN,L_TEXT);
    UTL_TCP.FLUSH(CONN);

while((tis.read(mybytearray)) != -1) {
                    }

while((tis.read(mybytearray)) != -1) {

Вот тут ничего не делается,
а должно быть.
Чтение из сокетного потока(у Вас это tis) и запись в Ваш получаемый поток.
Смотрите ещё примеры

                    }

OutputStream socketout = socket.getOutputStream();
                    //ByteArrayOutputStream pdfout = new ByteArrayOutputStream();
                    PdfConverter.getInstance().convert(document, socketout, options);

ByteArrayOutputStream pdfout = new ByteArrayOutputStream();
PdfConverter.getInstance().convert(document, pdfout , options);
pdfout.writeTo(socketout);

begin
	WHILE UTL_TCP.AVAILABLE(CONN, 2) > 0 LOOP
	l_result := UTL_TCP.READ_RAW(CONN, file_chunk_, chunk_size_);
	DBMS_LOB.writeappend(pdf, l_result, file_chunk_);
	end loop;
	end;

DBMS_OUTPUT.PUT_LINE('Size: ' || length(pdf));