I was able to reproduce your problem, without quite such a dramatic gap. Even when the labels in the tag family are set to have a transparent background, there still is a "zone" beyond the actual visible characters that is considered part of the extents of the label. In most tags, the linework is far enough away from the label that the linework forms the outer extents of the tag and the leader stops at the linework. But if the linework is close enough to the label, the label's extents can extend beyond the linework and the leader stops at the label, short of the linework.
The other possibility is that you have additional graphics in the tag family which are either assigned to the invisible lines subcategory or have their visibility tied to a parameter which is turned off for this view (or there is an emptyl label below the visible tag graphics). Even though these items are not visible, Revit will count them when calculating the tag's extents and stop the leader there.
David Koch
AutoCAD Architecture and Revit User
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