The reasoning is that as you gain information, you also have a duty to the people in the control group to use the best available information to take care of their health. Once you gain "enough" information ("enough" being statistically defined) that the drug helps, each additional person you let languish in the control group (who is denied access to the drug) is a cost that must be weighed against the benefit of getting additional information. When the data is clear enough, the cost can exceed the benefit, and you stop early.
Typically you'd register a "stopping rule" before you start your trial: a good drug often will trigger the stopping rule, as it helped so much that we learned about its efficacy on a smaller N than originally planned.
There are many different stopping criteria, depending on the trial (in safety trials you'd typically stop because you've found evidence that the drug is unsafe and continuing would be unfair to the folks in the treatment group, whereas in efficacy trials after safety has been established, you'd stop because you've found evidence that the drug is effective and continuing would be unfair to the folks in the control group).
Typically you'd register a "stopping rule" before you start your trial: a good drug often will trigger the stopping rule, as it helped so much that we learned about its efficacy on a smaller N than originally planned.
There are many different stopping criteria, depending on the trial (in safety trials you'd typically stop because you've found evidence that the drug is unsafe and continuing would be unfair to the folks in the treatment group, whereas in efficacy trials after safety has been established, you'd stop because you've found evidence that the drug is effective and continuing would be unfair to the folks in the control group).