I'm working on an indie game now, so as above, finishing means having it available for download/purchase. However, I'll be releasing in alpha, and then supporting/extending the game for as long as I can. It will only truly be finished when it fails economically and I can't afford to keep working on it ;)

As a professional developer, I don't think I've ever heard anyone talking about "finishing" a product.
You "release" it, but that is not the end of the line by far, you still have to market it, support it with updates, possibly run servers, answer user questions, maybe work on version 2.0, fix bugs on new hardware, etc, etc.
Then after a couple of years you might "stop supporting" it when you get too tired of it.
But you never "finish" software in general...

It's different when you're part of a work-for-hire developer, contracted by a publisher (not owned by a publisher). There are milestones throughout the process where you present certain work to the publisher, and in return they pay you money. Being late delivering a milestone may mean that the company can't afford payroll that month, and all the staff end up getting their own paycheques late :/

"Release" (or "gold") is the final milestone, associated with the final payment. After that, it's all the publisher's problem. Marketing, support, dealing with users is all done by them. The developer isn't being paid any more, so they've got no reason to care.

If an update/patch/DLC is required, the publisher will go back to the developer and negotiate some more milestones/payments. Again, as soon as this patch is complete, the developer is no longer associated with the product any more and has no reason to care about the product.

Some might say that the dev should care, because of the royalties that they'll get (basically an ongoing 'bonus' paid by the publisher to the developer based on the number of sales), but royalties are a joke in my experience... the largest I saw was $30k total royalties on a game that cost millions to produce (a few percent extra over the original invoice...), most other games I saw also cost millions to produce, and resulted in zero royalties due to the stupid conditions that are negotiated into the contract, so these kinds of developers only make money while working on new milestones.

This isn't because of "lazy developers" or greed; it's just business. They'll quickly go bankrupt if not working on paying jobs, so reaching the finish line as soon as possible is very desirable ;)