I believe what you are refering to is what is known as a land contract. The terms of a land contract are negotiated between the buyer and the seller. The terms of the land contract are usually not affected by the market going up or down. The only thing difference between a land contract and conventional forms of financing is the property is being financed by the seller as opposed to a bank, credit union, etc.. If you purchase a property under land contract, you have a set price, a set payment, a set interest rate and a set length of time for the contract. The value of the property may change but the terms of the contract don't.
There is , of course, a direct correlation between the value of the property and the owner's equity. If the property drops in value, the owner has less equity. If it drops far enough, the owner may not have any equity at all. If you would like to discuss this further, please feel free to call me at 920-655-8468 or email me at firstname.lastname@example.org.
I hope this answers your questions. Take care.