Yes, the insurance company that paid the insurance compensation has the right to take over the right of claim from the policyholder to the person responsible for the losses. In insurance law, this is called the right of subrogation.
If the flooding of your neighbor’s apartment was your fault, that is, if during the trial your specific illegal actions or inactions that caused losses are established, then the court will most likely satisfy the claim of the insurance company and recover losses from you. The amount of losses in this case is equal to the amount of insurance compensation paid.
The statute of limitations for such claims is 10 years from the date of the insured event.