• J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” J.~Symbolic Logic, vol. 63, iss. 2, pp. 549-554, 1998. ([HmSh:618])  
  Journal MR Citation arχiv

  @article {HamkinsShelah98:Dual,
  AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
  TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
  JOURNAL = {J.~Symbolic Logic},
  FJOURNAL = {The Journal of Symbolic Logic},
  VOLUME = {63},
  YEAR = {1998},
  NUMBER = {2},
  PAGES = {549--554},
  ISSN = {0022-4812},
  CODEN = {JSYLA6},
  MRCLASS = {03E55 (03E40)},
  MRNUMBER = {1625927 (99m:03106)},
  MRREVIEWER = {Douglas R.~Burke},
  DOI = {10.2307/2586848},
  URL = {http://dx.doi.org/10.2307/2586848},
  note = {[HmSh:618]},
  eprint = {math/9612227},
  archivePrefix = {arXiv},
  primaryClass = {math.LO},
  }

After small forcing, any $<\kappa$-closed forcing will destroy the supercompactness, even the strong compactness, of $\kappa$.