With Scrum implementation, you will have a set of Stories with associated tasks to complete within a fixed time frame of approx. 2-3 weeks. Now, if anything new arises for the team to work on it should be prioritised for the next Sprint (assuming it can wait for this time). Otherwise someone has to make a priority call on it and whether the team should work on the new piece within the current stories. A stakeholder (PM) could move a lessor priority story for next Sprint, if that is possible. Otherwise all the stories should be completed within agreed time frame.
Alternatively you could set a Support process up between Development and the Customers (in they are not thousands of them) and allocate some of the team's time to it and work on these tasks in parallel with the assigned planned Sprint Stories.
