We live in a small apartment and have a new furnace heater which feeds
the hot air through a simple duct system. The heater is in one of the
closets and the ducts are insulated with what looks like some type of
soft aluminum foil wrapped around some cushy insulation. In a couple
of spots, there is wrapped also some of that soft, fluffy insulation I
guess to reinforce the areas where the ducts meet.

(Well, you can already see how sophisticated my knowledge is about
home improvement.)

A few times our cat got into the closet and used the insulation as a
scratching post -- so there are some tears in the soft tin foil part.
She also pulled apart the soft fluffy insulation where it was used
outside of the ducts.

Finally, she actually caused an elbow where the dicts meet to come
apart so I had to refasten it.

My question is, considering that her claws did only minimal damage to
the insulation, is there any danger in running the heater?

Also, does the soft fluffy insulation pose any kind of threat? I mean
is it like asbestos or anything?

Thanks in advance for any knowledgeable input!