What would happen if a piece of code from a proprietary source was uploaded by someone without permission to github with the MIT license and thousands of people have used it. Even if the company who owns the code requests github to drop the repository, what would prevent the endless spread of the code by users believing it to have MIT license. What should the owner do in such cases to prevent it from happening?
If it was something important to the owner, they would file injunctions/suits against everybody that they find the code in, and make those very public. This isn't unlike what the RIAA did to individual downloaders of pirated music files, filing over 18,000 lawsuits. They could subpoena GitHub for information related to IP addresses for who downloaded the code and go after them. It is unlikely that they would get a financial award but they could have the court order them to stop using it.
Eventually the RIAA found that filing these lawsuits was more trouble than it was worth and started going after the internet service providers. These reduced the number of lawsuits and forced ISP's to moderate its own users, blocking some sites and protocols that programs like Napster relied on. Basically they shifted responsibility from themselves to the ISP's.
Legally, everyone downloading the software would be committing copyright infringement. You could sue the uploader for statutory damages (maximum $150,000) or actual damages; people who have worked years to collect some wealth usually don’t do that kind of nonsense, so you might win a judgement but most likely won’t collect any damages because there is no money.
GitHub uses the Git software which makes it possible that anyone who downloaded your software and then tries to download a newer version will have all illegal files on their own computer automatically removed with one file left explaining what happens. Since Github is a company with money that could be sued for helping with copyright infringement and could be made to pay, they will help you. What I described is easily circumvented but would turn the downloader from an innocent person who was tricked into committing copyright infringement into a deliberate infringer if they do that.
As a result there is likely to be very little commercial use of your software. People who would want to use it will very quickly figure out that it is legal poison, and important for a commercial user is also the fact that there will be no updates ever.
Should you find out at some point in the future that a money-making product uses your code illegally, you could sue them for copyright infringement or offer an (expensive) license which to some degree they would have to accept.