Generally speaking, a future change to the code's license does not impact the license under which you received the code. If you validly received some code under the MIT license, and later the author stops offering the code under the MIT license (and offers under the GPL instead, or stops offering it altogether), that does not change the fact that the author granted you free use of the work under the MIT license.
If you did not receive a copy of the license text when you received a copy of the work, you still have permission to use it under that original license grant. However, you may have difficulty proving it, if the owner destroyed all evidence that they used to offer the code under a different license in the past. Determining whether you recieved the code under a particular license would be a matter of evidentiary fact-finding by the court, if legal action ensued. If the court found that the author really did offer you a particular license, then you are free to operate under those license terms, whatever they were at the time.
By linking to a license page, the author can easily say, "I am currently offering the code under whatever the license text on this page says." This makes things easy for the author, but more difficult for users who want to verify the exact terms of their license (as the current posted license terms may change to differ from their received license). If the software doesn't include one, users should save a copy of the license grant they received at the time of download, if they wish to refer to it in the future.
It may be possible for the copyright holder to proactively revoke a license grant to some user. I am not sure exactly how to do this, but I imagine the copyright holder would need to directly contact license recipients and inform them that their license grant is terminated. Whether this is a legally valid thing to do probably depends on the exact relationship between the licensor and licensee (is there payment or a contract involved?), how the licensor offered the software (did they explicitly say they reserved the right to revoke the license?), and the exact terms of the license (e.g., the GPLv3 is explicitly irrevocable). There is U.S. case law that strongly indicates that software under an open source license offered to the public at large can be (and may often be) irrevocable by default; see Are licenses irrevocable by default?
Regardless, revoking a license is very different from merely changing the license an author offers to future recipients.