Damage to owners unit

The first step is for the owner to contact their own respective home insurance and let the professionals sort through the details. The HOA doesn't need to get involved until the owner's insurance asks.

Yes, the board should get involved to assess the damage, see if the common elements (such as the subfloor, perimeter walls, etc) were affected, and make sure it gets dried out and fixed before mold spreads to other units.

The Illinois Condo Act requires the association to carry insurance on the units and for the association's insurance to be primary. This means that the association's insurance should pay for the damage to this owner's unit. Maybe you didn't do that last time, but it is the law. To be fair, I did not read up on the law to see if there are any exceptions. You can discuss it with the your insurance adjuster.

What about the deductible? The association's deductible can be paid by the unit owner's insurance. In other words the association only needs to pay out what it gets from the insurance claim, and does not need to pay for all the damage. The unit owner's insurance typically pays for anything that is not paid by the association's insurance. The unit owner will have to pay for their deductible.

What everyone else said - that's why insurance was invented.

Here's hoping the homeowner with the leaking sink had water/sewer line damage coverage - usually, this isn't part of a standard homeowner's insurance policy and you have to buy it separately. Otherwise, that person is looking at several thousand dollars worth of liability.

You might want to encourage your homeowners (all of them) to discuss coverage with their insurance companies. Better yet, check with your association master policy to see how they look at this type of damage - sometimes this type of news goes over a little easier if it comes from the master insurance carrier and the homeowners don't think the board's making up stuff because they don't want to pay.