How to fix a crumbling stoop?

I'm not sure how to fix crumbling concrete, but you could remove the concrete and install some pavers.

Build a deck like wood section over it.

Marilyn....Since it is so small I would agree that I would remove and then do the pavers.

It’s not going to be fixable, sorry.

You can build a mini deck on top of it, with treated lumber. That would be cheap and easy. Use coated decking screws.

I would make it wider and make sure the dirt near the house drains well away.

I would anchor the frame of the deck to the house foundation with TapCons and Liquid Nails (exterior).

The thing is, since it's crumbling, the surface has already been compromised - and probably not by just this winter's weather - but many before. If replacing the slab it too much, then you have to do a makeover. Clear off the debris and use a concrete patch to fix the top and edge. Then you're going to need to seal that whole slab top. There are lots of products that will seal concrete - follow the directions paying special attention to the weather/temperature when you're applying. That will help stabilize it. Now, to prevent future crumbling, you could box the area in and add pavers or flagstone & pebbles, blacktop or some other product you like that will give traction but stay in place during all your seasons. Heck, you could even paint the concrete before you seal it. If you use a heavy outdoor epoxy for the seal you can both color it and add sand which will give a rough surface. You have a LOT of options. Find what will work best for you!

When you are considering options to replace the crumbling slab my advice to you is to get professional appraisals of the overall condition of this entrance.I expect you have noticed the central crack in the concrete threshold under the door? As it is your front entrance, and it seems to connect to the driveway, a thoughtfully considered walkway and wider area at this entrance to your home should be worth additional planning and expense. Do you get snow? maybe a boot scraper to make coming in to your hallway a 'drier' experience. A much more substantial (larger and well swept) exterior mat will keep dirt and water outside as well. Please don't think small, think function and beauty; you won't regret doing a proper job of it.

You most certainly need to do a proper fix/replacement! Should anyone be injured on these steps, you will be legally responsible for all "damages" including things such as medical bills, lost wages, etc. Though your homeowners insurance may assist with this, depending on what type of coverage you have you could end up in a situation where the legal costs to you may cause you to lose your home or other catastrophic consequences!