My house sits atop an unfinished, drive-in basement workshop/2 car garage. Built before regulations required sheetrock ceilings, floors to the living space above are insulated with unbacked fiberglass batting. Over time this insulation has become dusty/dirty. In places the insulation "strings" hang down like stalactites. I don't want to just replace this insulation. I understand backed nor sleeved insulation, or even foam board products, can be used due to flammability. Other than sheetrocking are there any other options to be consider?
Thanks

Is the insulation really unbacked, or is the vapor retarder up against the subfloor above, as it is supposed to be?

If it is really unbacked, I would remove it, install new insulation with a proper vapor retarder, and then install Type "X" gypsum board on the ceiling, all walls, and over any structural element such as wood girders.

This is a life safety issue, and whether it was required or not when your house was built, I blieve it makes sense to update this part of your house to conform to current codes. Why take a chance?

As usual, Rich is right on the money.

It seems you have two issues. First, the insulation is installed in the ceiling for energy efficiency (obvious). The paper backing should face the heated side to act as a vapor barrier, preventing condensation in the insulation.

Second, you have a fire safety issue. The recommnended practice is to install wall/ceiling covering to prevent/slow the spread of fire from the garage into the ceiling joists/wall and thus the living area of the house. I believe the material is rated for 1/2 hour burn-thru time. 1/2" thick drywall is normally the easiest due to cost of material relative ease of installation. Joints and seams should be taped, again to slow fire from spreading through the cracks. They don't have to look pretty, just seal the common walls between the garage and living area of the house.

Paneling, pegboard, plywood, etc. is generally not recommended due to lack of fire resistance.

You might as well gyprock now when you're doing the renos; otherwise if you ever have to sell your home, they may make you do it then.

And there are other issues, generally because just slapping insulation in a space isn't going to solve anything. Any idea why your insulation is dirty and dusty? Where is this dust coming from? Where is it going to? It's evidence of an air stream coming through the garage and probably into your house through this floor. And it's bringing crap that shouldn't be coming into your house:

HGTVPro Video on Garages
HGTVPro Article on Garages

Fortunately, all this air sealing will actually solve a lot of the standard insulation problems anyways.

I was reading over the ICC Code Change summaries from the 2004/2005, and there was this proposal that the insulation manufacturers had put in to increase R-Value requirements over garages to ceiling levels in order to solve cold floor issues.

It got denied.

And the committee reason (and I paraphrase):
"This committee recognizes that adding insulation to the underfloor space doesn't solve anything. Without any requirements for air sealing, this proposal is only a partial solution."

EC-15, 2004/2005

Ugh, I just spent a half hour of my life that I will never get back finding that code reference. I hope you actually appreciate this information, and don't blow me off.

I am only too happy to ditto the remarks of Richard, Mark, and Doug, with a few added remarks of my own.

First, prior to re-insulating and sheet-rocking your garage ceiling, you may want to ensure that any pipes are wrapped in foam sleeves, to prevent condensation from occuring when warm, moist air contacts the cold pipe(s).
Second, any ducts in the ceiling should have all seams and joints sealed, so that air leakage doesn't pressureize the ceiling space, especially if you have central air conditioning, as this could create a mildew problem when cold air escaping from the ducts causes the warm, moist air in the un-conditioned space to condense on the ceiling, much like a cold glass of lemonade causes condensation, and puddling of the condensate, on your table in the summer.
Third, any electrical problems, or upgrades, should be accomplished at the same time, making certain that armored electrical cable, which is zinc-coated steel, doesn't come into contact with any copper. The two dis-similar metals are at opposite ends of the galvanic scale, and a measurable direct current is generated when the zinc cathode is in contact with the copper anode, causing the copper anode to be eaten away. This is the opportunity to get those outlets, switches, and lights put in where you really want them.
Forth, remember that it is a code violation to bury an electrical junction box behind a wall or ceiling. The junction boxes must always be accessible.
Fifth, the same would hold true for plumbing valves or clean-outs. Access panels would allow you to cover over any of the above, or, you could drop the junction boxes and valves below the ceiling.
Sixth, 1/2" gypsum only provides a 20 minute fire rating. Use the 5/8" type X that was recommended, since you then will have a 45 minute fire rating.
Hope this helps.