In an agile software development team, who would be the one to fix the bugs introduced in an update?
In an agile software development team, one hopes the notion of code ownership doesn't exist. In such a team, collective code ownership should reign supreme.
In such a team, the person to fix the code is the first person to notice the bug - either due to their own testing, a report from another team (say testers) or a customer. Every member is just as competent to fix any bug as anyone else.
That also means that bugs don't languish, waiting for person X to come back from vacation. Or if person X has gone from the company, there are others that can pick up without trouble.
(also see the different definitions discussed by Martin Fowler)
Assuming you are not working in such a team - still anyone should pick up the bug. And verify the fix without someone in the know.
The developer who writes the feature?
Possibly. If no one else can possibly fix it. Many bugs are trivial and can be fixed by anyone. Having collective ownership means that whoever fixes the bug gets to learn about the new bits of code - so more than one person can work on that bit.
Someone else specialized specifically in debugging with a certain title?
I've never heard of "senior debugger" positions. Hope to never hear of them. Frankly, debugging is part of the job. Everyone should be able to be effective at it.
The best developer in the team?
Poor fellow. Wouldn't do anything but debug stuff all day. Wonder how long it would take that person to quit.
Oh. And who decided on that? Kinda subjective, not to mention political.
Again - everyone in the team should be comfortable debugging and fixing any piece of the codebase. Or if not everyone, most people should.