A couple of months ago my rental had a window leak that did damage to my tenants China cabinet. I saw that the reason for the leak was because they did not secure the window properly which was why that window was the only one leaking. Now that my tenants have moved out, they want me to pay for the damages. Who is responsible for the damages?
Renter's insurance (if they had it)
So they left the window open and it leaked but that is your fault? If the latch is broken and the window won't properly close then it might be your problem. My lease actually reads that it is the tenants responsibility to notify me of problems like a leaky pipe or broken window in a timely manner otherwise they are responsible for damages. I feel that if they failed to notify you of the defective window and you had no way to know it was defective or if they just failed to close it properly then it is their fault and they should file an insurance claim or pay for it themselves. If they told you the window was broken and you refused to take care of it in a timely manner then it is your fault.
That is totally their responsibility. If anything, I agree, maybe their renter's insurance policy will cover it. Also, if they were so concerned about the cabinet they should have discussed this with you before they planned to move out. The delayed request seems shady. I hope you took pictures of the opened window that caused the leak.
Tenant is responsible unless they can show it was the fault of you or the property. Sounds like you already know the answer.