It's probably best to have them pay out of pocket for a smaller cost like this.

I am mostly interested in appreciation/pay out at the end rather than cash flow each quarter.

This designation doesn’t cost extra or give the manager access to insurance payouts but ensures you and the property manager are aligned during incidents, such as tenant lawsuits or insurance claims.

Aircover does not always agree with you and pay out.

I need funds (but only for the buyout portion of the deal, and she's agreed to certain percentages).

After talking to another family member they said they would be willing to go in on the duplex and offered to pay the $40,000 down payment and help with any repairs but they want to be "partners" or "own" a percentage of the duplex.

This ensures that any payout for damage or liability can be processed more smoothly, and it can help protect your interests if something happens on the property. 

Suggesting to them buying their house for a wholesale range offer or lower dependent on the extent of the rehab, then having a contract in place that gives them a percentage of the profit to help get them back on their feet, paying off debts etc.

Insurance would cover it, I would pay the deductible, and no assets would be lost.If you are in an area like San Diego where people are more likely to sue, a judge is more likely to find you guilty, and the payout is expected to be higher, you may consider an umbrella insurance policy.

What off-market really means is that the seller refuses to sign an exclusive listing agreement with an agent but tells the agent if they bring them a buyer, they'll payout a commission.