If you install ncurses-devel-5.6-20.20080927.fc10.i386 which is the latest released fedora core 10 version. Then the file /usr/lib/libtermcap.so is a text file containing INPUT(-ltinfo) Instead of an actually shared library. I'm also guessing there should a /lib/libtermcap.so.<something> which doesn't exist at all.
libtermcap was dropped few releases ago and all applications should use libncurses (or libtinfo directly) instead. The .so file should allow linking with libtinfo where -ltermcap is used.