The client can always use their own funds to replace debt. 

We all invest in real estate in order to make money, and keep in mind that someone who can only afford to live in a mobile home and seller-finance to buy the land is probably tight on funds. 

-> Funding: you can consider as options mortage brokers who can scout/compare the best offers in the market and you can also consider public funding programmes that exists as an incentive to renovate and bring houses to the market, either for tourism or traditional rental.As an example, on the traditional rental there is a funding program ("Arrendamento Acessivel") that funds up to 90% of the project and can be used to cover part of the renovation costs, as well as, part of the purchasing.

Any other expenses are using up funds that would otherwise be sitting in your checking account to make a mortgage payment with.

From what I've learned it seems that a HELOC is probably the easiest way to gain funding but at the same time it comes with risks if the flip isn't successful. 

Lender wanted homeowner to sign something to recieve the funds.

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.

Both properties have a substantial amount of equity that’s essentially sitting idle.Would it be a good idea to tap into this equity (through a HELOC, cash-out refinance, etc.) to fund future fix-and-flip projects or purchase additional rental properties?

I'm also a licensed mortgage broker with a lot of fix-and-flip programs, including some that require as little as 10% down on the purchase price, and provide 100% of the rehab funding.

Bronson Hill created at fund of funds and invested through Dave Zook at the RealAsset Investor.