My parents live in a house that is over 100 years old. In the middle of the house it is sagging. It was like that when they bought it and were told it wasn't an issue. My mom claims it hasn't sunk further into the ground since they have lived there but not sure if maybe she hasn't noticed cause they've lived there a long time or what. When I asked if she was going to have it repaired she said it was going to be too expensive and not worth it. She thinks because it hasn't fallen in on itself in the last 100 years it won't. Will it fall in on them? Should she look into having it fixed no matter the cost? They have a second story home and a dirt floor basement.

We would have to ask you too many questions and you wouldn't have the answers, so there's no way to know.
Chances are it isn't going to fall on them - usually other problems are evident years before it would, such as roof leaks.

Unless your parents are of concern in all areas of general negligence of their house and themselves, I would let them be the owners and leave it at that.
They could have two or three contractors look at it for free.
One scenario I can imagine is that some of the middle posts in the cellar, being on dirt, have sunk.
The fix would be concrete piers and new posts next to the old ones, installed after jack posts slowly raise the main beam.
That would be low thousands of dollars, depending on how many posts are needed.

Better to ask a qualified foundation contractor---"Will it fall in on them?"

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They could have two or three contractors look at it for free.

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Better to ask a qualified foundation contractor---"Will it fall in on them?"

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That's where you start for the FACTS.

There's facts and there's facts.
E.g., many a homeowner will take the cheap fix, such as putting a couple of lally columns under the beam, resting on a patio block or two... save thousands.
Will the house fall down on them? Probably greater odds of the tectonic plates shifting under them.
Look how many of us live with odds like earthquakes, mudslides, tornadoes, and whatnot.
Then there's the facts that a contractor will tell you... how do you know they are telling you facts? You don't. They want the job.

There may be homeowners insurance, or some sort of financing plan also, just in case. The point of getting facts is to know the options so you can make a reasonable decision. Joy is correct contractors are looking for business, but talking to many may make you more aware of what is needed. The ultimate responsibility is your parents, but maybe you can do the footwork, and gather facts for them.

Maybe this type of thing is covered under the homeowners policy, and they have contractors they work with. Just do the best you can to address your own concerns for their safety.