Can wet insulation stay in the ceiling or wall and dry on its own?

Do not assume that closing it back in is adequate. EPA's clean-water response table recommends discarding and replacing wet cellulose and fiberglass insulation. Ask the contractor to identify the insulation, show the affected area and explain how the surrounding cavity will be dried before replacement. Other insulation products need their own assessment. Contaminated water or existing mold calls for a different cleanup plan, not simply more time with fans.