Kinetochores that are not attached to microtubules prevent chromosome missegregation via the spindle assembly checkpoint. We show that they also promote their own capturing. Similar to what governs the localization of spindle assembly checkpoint proteins, the phosphorylation of Spc105 by Mps1 allows unattached kinetochores to sequester Stu1 in cooperation with Slk19. The withdrawal of Stu1, a CLASP essential for spindle integrity, from microtubules and attached kinetochores disrupts the organization of the spindle and thus allows the enhanced formation of dynamic random microtubules that span the nucleus and are ideal to capture unattached kinetochores. The enhanced formation of nuclear random microtubules does not occur if Stu1 sequestering to unattached kinetochores fails and the spindle remains uncompromised. Consequently, these cells exhibit a severely decreased capturing efficiency. After the capturing event, Stu1 is relocated to the capturing microtubule and prevents precocious microtubule depolymerization as long as kinetochores are laterally or incompletely end-on attached.