cipher text only attacks on deterministic homomorphic encryption schemes
This is an interesting question. If the input set does not have any identity element (for both mul and add operations) then one cannot construct a field and subsequently there cannot be homomorphic operations.  More clearly, if the input plaintext elements do not form a field (and their respective ciphertext elements do not form a field either)  then there cannot be homomorphisms of operations. This is by definition of Field.

So if the input set contains identity elements (and other properties needed to become a field) then while the given set members may not have any obvious relation. There would be some constant $c$ for which  $enc(n_1) + c * enc(n_2) = enc(0) $ subsequently finding which attacks mentioned in previous question apply ! 

Also  an attacker could try to find random complex relations among them. For example is $ enc(a) + enc(a) = enc(b) $ or is $ enc(a) *enc( b) = enc(c) $ etc. revealing inferences.