What issue arises in the Senate due to off-topic amendments to bills, which can lead to a bill not passing?

The issue that arises in the Senate due to off-topic amendments to bills, which can lead to a bill not passing, is known as riders. Riders are amendments or provisions added to a bill that are not directly related to the main purpose of the legislation. These can be controversial or unpopular issues that some senators attach to a bill to secure their passage or to force a vote on a particular issue. This tactic can complicate the legislative process, as senators may be reluctant to support a bill if it contains riders that they oppose. If the primary purpose of the bill is overshadowed by these additional provisions, it can lead to negotiations and conflicts that ultimately prevent the bill from advancing.

In contrast to riders, other concepts like the filibuster and cloture specifically deal with the procedures of debate and limiting discussion, while a pocket veto relates to the president's ability to take action on a bill after Congress adjourns.