/usr/lib/libsolidcontrolnm09.so.4 is in plasma-widget-networkmanagement 0.9.0.1-0ubuntu2.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/libsolidcontrolnm09.so.4.8.0
/usr/lib/libsolidcontrolnm09.so.4.8.0