If a black hat gets crushed on Shabbos can one fix the hat back to its wearable form?
It is permitted to straighten out the hat.
Or Le’Zion (27:9) writes that if the hat is crushed to a point that it cannot be worn, it should not be fixed up on Shabbos, because this could constitute tikkun mana. However, Chazon Ish (Dinim Vehanhagos 13:17), Rabbi Shlomo Zalman Auerbach (Shemiras Shabbos Kehilchasah 15:47; Me’or Hashabbos 1:11, no. 8) write that for a soft (felt) hat it is permitted to straighten out the hat. See also Yalkut Yosef (2:15, p. 81), who is likewise lenient, and Orchos Shabbos adds that Rav Elyashiv also rules leniently on the matter.