Need an Introduction to Tiny Core? Or peruse Core Concepts.
/usr/local/lib/thing.so /usr/local/lib/thing.so.1 /usr/local/lib/thing.so.1.0.0
When you load the fs, it will copy those files from the tcz into those directories.
But is ld.so.cache automatically updated? If it isn't then the loader should not be able to find them.