If fiberglass batts of insulation are to be left exposed, they should be unfaced. Both fiberglass and mineral wool are naturally fire-resistant. At high enough temperatures, they may melt; but they do not ignite, minimizing the risk of a fire spreading.
Fiberglass batts have passed the requirements of the American Society for Testing Materials’ E136 test on combustibility. They are classified as noncombustible in all major building codes.
Faced insulation batts are those that come with one side covered by a layer of either foil or kraft paper. Both are affixed to the insulation using asphalt-based adhesive. Such facings, intended to act as vapor barriers, may also serve as deterrents to burrowing insect pests. However, faced insulation should not be left exposed, as both the foil and paper facings are combustible and may ignite if exposed to high enough temperatures.
If your unfaced insulation is not exposed, it is advisable to fit a vapor barrier over it. Both fiberglass and mineral wool will retain moisture if exposed to it. This will pack down the insulation and reduce its effectiveness as a thermal barrier. Foil and kraft paper are available as separate facings that you can affix over batts. Polythene plastic, plywood, drywall and plastic-coated insulated foam sheathing are other options.
Fiberglass insulation is a hazard to health if it becomes damaged. If fibers become loose they can irritate the skin and affect breathing. Inhalation of fiberglass dust can exacerbate existing respiratory conditions such as asthma. When handling fiberglass insulation also wear protective gloves and a face mask. If any exposed fiberglass insulation gets damaged, replace it.