While I understand your motives, it's not how you'll succeed.
A game, it's a story before being lines of code. Have you seen many book writers going around and asking to buy an unfinished book ? No, because it wouldn't works.
To make a game, you need to develop its story, and if it's not yours, how can you do it ? You'll not know the unspoken motives of the characters, nor their personality, so you can't write accurate dialogs, nor have accurate reactions. Because of this, you'll also don't really know from where the story come. And like you don't know the story tracks, you'll also don't know where the story is going.
The chances that you'll have all this when buying a project are extremely low. If the author was dedicated enough to know all this, have precisely built the story board and the characters, and therefore have enough material to give you so you can appropriate the story, he wouldn't have abandoned the project this easily.
So, in the end you'll end abandoning the project yourself, because you struggle with it and quickly discover that you aren't in capacity to write something coherent enough to effectively interest players.
In the days before self-publishing, kindle, amazon, etc. That's exactly how it worked. Writers sold their unfinished story to a publisher. You say yourself, that games are based on a story, so you recognize that the story comes first, before the game.
But then you imply that someone out there might start making a game without a story, and it would be impossible for a publisher to finish the game. If you opened a patreon with no story, more power to you, but usually a game doesn't get started without the story. Turning a story into a game usually starts with a GDD which serves as the initial game copyright and blueprint, also complete befor the game is started.
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Once upon a time I had the unpleasant job, of reviewing potential game ideas that people wanted to sell to a game studio. More often than not this meant showing people that their great game idea already existed, crushing their hopes and dreams. Occasionally a brilliant idea would come along, and even in it's roughest form you could tell it was a diamond.
Adult Games get abandoned for all sorts of reasons, usually financial, or family, not because the story is unfinished, but because the work is unfinished.
It sounds like OP is interested in becoming a game publisher. If they have the resources to finish a project, and someone has a project with one foot in the grave, it could be win-win.
