All FHE schemes today add tiny random noise to the ciphertext so that encrypting the same data twice give different results. The noise is then kept to a nominal level as you compute homomorphically using a special operation called bootstrapping. Then when you decrypt, you just ignore the noise and get your result. If you do that well and dont let the noise grow too big, you get very strong security.

Fwiw, bootstrapping is actually what makes FHE slow, not the actual addition/multiplication etc