Which of the following terms describes the insurer's right to take over property to offset a loss paid?

The correct term that describes the insurer's right to take over property to offset a loss paid is the subrogation clause. This clause allows the insurance company to pursue a third party that caused an insurance loss to recover the amount it paid to the insured. By exercising this right, the insurer can reclaim some or all of the financial loss by taking ownership of the damaged property or by seeking reimbursement from the liable party.

Subrogation is a fundamental principle in insurance, ensuring that the insured does not benefit from a loss while also allowing the insurance company to mitigate their expenses. This maintains balance in the insurance process as it prevents the insured from receiving compensation from both the insurer and the responsible third party for the same loss.

The other terms mentioned are distinct from this process. Casualty refers to types of insurance that cover loss or damage to property or liability for damages caused to others. A deductible is the amount the insured pays out of pocket before the insurance coverage takes effect, while property insurance is a broad category of insurance that covers different types of property but does not specifically address the insurer's right to recover losses.