The example given in the spell specifies that "dirt" is ok. I feel as though this line is being taken out of the context it's written in. Here is the full context.

The wall doesn't need to be vertical, or rest on any firm foundation. It must, however, merge with and be solidly supported by existing stone. Thus, you can use this spell to bridge a chasm or create a ramp. If you create a span greater than 20 feet in length, you must halve the size of each panel to create supports. You can crudely shape the wall to create crenelations, battlements, and so on.

As long as the stone wall is merged with and coming out of a stone from which the wall can be made, it seems that are ok. I can't imagine that there exists a chasm which is pure stone without dirt, from which the spell is describing when it says you can create a ramp or bridge out of the wall.

As an evocation rather than a conjuration spell, it makes sense that the wall might require some stone to work with. This has been confirmed by Mike Mearls, that some sort of rock is required:

‏@wax_eagle : @mikemearls Can Wall of Stone be cast on dirt? It seems like its written to always need stone to merge to. Is that correct?

Mike Mearls : @wax_eagle that's correct - need some stone to merge with or be supported by. for instance, a bridge is OK if the two ends touch stone.

Daganev : @mikemearls @wax_eagle So no stone walls on a grassy knoll?

Mike Mearls :@Daganev @wax_eagle Correct, you'd need rocks of some sort (ruins, boulders) to support it.

Almost any creature could escape before suffocating

In most circumstances, the victim would have ample time to chisel their way out.

Wall of Stone creates 10 foot panels (or larger). So let’s assume: (1) your spellcaster trapped their victim in the minimum size, 10' cube, and (2) they concentrated on the spell for 10 minutes, making the stone permanent.

I’m not aware of any rules that would cover suffocation in these conditions, so let’s fall-back on real-world facts. This Friday Fiction Facts: Trapped in an airtight room! article calculates it would take hours]for a person to suffocate in those conditions

“A moderately active or stressed person” would have about 17 hours until they experience symptoms such as “panting, dizziness, severe headache, vision disturbances” at which point we will assume they can not longer effectively chisel at the wall.

The wall is an object made of stone that can be damaged and thus breached. Each panel has AC 15 and 30 hit points per inch of thickness.

At 30 HP/inch times 6 inches, the victim needs to do 180 HP of damage to the AC 15 wall to escape.

Let’s assume our victim is a human commoner with no strength bonus. We’ll even take away their club listed in their stat block, and just give them an improvised weapons, with which they get no attack bonus. Each round, they can do 1d4 points of damage to the wall if they “hit” with a roll of 15 or higher.

With those assumptions, the commoner’s average damage-per-round would be 0.75 HP. On average (and with this many “rolls,” most attempts would be very close to average) it would take 240 rounds to chisel out.

A round is 6 seconds; there are 600 rounds in an hour, so our mild-mannered commoner can chisel free in 0.4 hours, or 24 minutes.

• (240 rounds) / (600 rounds per hour) = 0.4 hours = 24 minutes for a commoner to escape

So even if we make assumptions that our victim needs to rest three-quarters of the time they still get out with hours to spare.

If you are trapping an armed and dangerous creature, they are likely to be able to escape in even less time.

Edge cases

It’s easy to come up with edge cases where someone would not be able to dig out, or if the wall were made double thick, or more (which would require a lot of time since you have to concentrate for 10 minutes for each effect). In these cases the rules pretty much silent (the Portable Hole mentions death by suffocation in an enclosed space, but that’s a pretty different case).

Would there be tiny cracks in the wall, or the floor beneath it that allow air to seep in (like there are in the building where you sleep)? I think that is simply up to the DM. This is a world where you can breathe miles deep in the Underdark — the whole “how do we breathe” issue gets a little glossed over.