How can a fully encrypted homomorphic program resist copying? Let's say that we have an original homomorphically encrypted program with any possible code inside. What methods can it use to ensure that it is impossible to create an exact copy of it? Are there such ways?

I understand that a person without a key will not see the internal content of a homomorphically encrypted program, I'm interested in whether it is possible to limit the exact copying of this program entirely.
Homomorphic program encryption, assuming you want it fully operational, is not possible. At some point of time actual operations are executed (directly or in obfuscated form).
Encryption of any kind does not prevent copying, because with physical access to hard drive you can make verbatim copy at any moment.
There is also a huge slowdown with program obfuscation (like in Gentry's garbled scheme)/communication that drastically reduces realistic use.