For example, if she can't visit the property, is she good at record keeping (so everything is organized at tax time) or finding vendors, comparing product prices, finding free or low cost items on Facebook marketplace to improve the rental)3. emergency fund.

Are you looking to pay off the hard money loan, fund another investment, or cover property improvements?

But if you are for example funding the improvements out of pocket, you will want that initial value. 

I think the uneasiness comes from not having enough reserves/ funds for downpayment and closing.

Donating money to large (FEMA, Red Cross), local organizations or Go Fund Me pages would be the quickest way.

If the loan was fully funded at closing and since then the loan is in an interest-only payment period, these numbers would equal. 

You can reach out to the Title company and see if there are any funds remaining for dispersement, if so then ask if there is a way to make a claim to those funds.

Lender wanted homeowner to sign something to recieve the funds.

Banks like proof the funds were in a bank well before closing. 

Do you use your own cash or do you have a lender or investor funding your deals?