In the first part of the talk I will review the scenarios proposed by
Hubeny and Jacobson-Sotiriou that suggest that a near-extremal black
hole can be turned into a naked singularity by absorbing a
particle. In the Hubeny case, the black hole is charged, and it
absorbs a particle with sufficient charge to produce an overcharged
final state. In the Jacobson-Sotiriou case, the black hole is
spinning, and it absorbs a particle with sufficient angular momentum
to produce an overspinning state. I will explain why such scenarios
violate the third law of black-hole mechanics (although there may be a
loophole), and seek a mechanism that prevents such overcharged or
overspinning final states. I will argue that self-force effects on the
particle could provide this mechanism, and describe earlier partial
attempts to incorporate the self-force into the scenarios. In the
second part of the talk I will describe ongoing work with Peter
Zimmerman on the formulation of the self-force when the background
metric is not a solution to the vacuum field equations (which is the
case when the background spacetime describes a charged black hole).