En esa región viven setecientas familias y muchas trabajan en el campo.

Both are possible, but viven setecientas familias is very natural in Spanish after a place expression like En esa región.

Spanish often uses this word order:

• En esa región viven setecientas familias.

This structure puts the location first and then presents what exists or who lives there. It sounds a bit like:

• In that region, there live seven hundred families.

If you say:

• En esa región setecientas familias viven,
  it is not the most natural option in normal conversation.

You could also say:

• Setecientas familias viven en esa región.

That is correct too, but the original sentence flows very naturally in Spanish.

Because familias is a feminine plural noun, and the hundreds from 200 to 900 agree in gender with the noun they modify.

So:

• setecientos libros = seven hundred books
• setecientas familias = seven hundred families

This agreement is normal with Spanish hundreds:

• doscientos / doscientas
• trescientos / trescientas
• cuatrocientos / cuatrocientas
• etc.

But note that mil does not change:

• mil familias
• mil libros

It is an irregular form, so it is best learned as a whole word.

The pattern is:

• 700 = setecientos / setecientas

Compare:

• 600 = seiscientos / seiscientas
• 700 = setecientos / setecientas
• 900 = novecientos / novecientas

So setecientas familias means seven hundred families, with feminine agreement.

Because muchas is standing in for muchas familias. Spanish often leaves out a noun when it is already clear from the context.

So:

• En esa región viven setecientas familias y muchas trabajan en el campo.

means:

• In that region, seven hundred families live there, and many [of those families] work in the countryside / in farming.

This is very common in Spanish. For example:

• Tengo dos hermanas y una vive en Madrid.
  = I have two sisters and one lives in Madrid.

Here, una means one sister, just as muchas here means many families.

Because it refers back to familias, which is feminine plural.

Spanish words like mucho / mucha / muchos / muchas must agree with the noun they describe or replace.

So:

• muchos hombres = many men
• muchas familias = many families

Since the noun is omitted but still understood, the agreement remains:

• muchas trabajan en el campo

That tells you the hidden noun is feminine plural: familias.

Here en el campo usually means in the countryside or in farming / agricultural work, depending on context.

With trabajar en el campo, the most natural meaning is:

• to work in the fields
• to work in agriculture
• to do farm work

So in this sentence, it suggests that many of those families work in agriculture or rural outdoor work.

It does not usually mean just any kind of work done outdoors. It strongly suggests a rural, agricultural setting.

Esa is a demonstrative adjective meaning that.

Spanish has a three-way contrast that learners often notice:

• esta = this
• esa = that
• aquella = that over there / that more distant one

So:

• esta región = this region
• esa región = that region
• aquella región = that region over there / that distant region

In modern Spanish, especially in everyday use, ese/esa often covers the normal meaning of English that.

Vivir means to live, to reside, or to dwell.

In the sentence:

• En esa región viven setecientas familias

the place phrase En esa región has simply been moved to the front. The full basic idea is:

• Setecientas familias viven en esa región.

So yes, vivir still normally goes with en when you mention a place:

• Vivo en Madrid.
• Muchas familias viven en esa región.

The original sentence just changes the word order for a natural Spanish style.

Grammatically, in this sentence it refers to familias, because muchas is feminine plural and matches familias.

In English, we might naturally think of the people in the families doing the work, but Spanish is expressing it through the noun familias:

• many families work in the fields

That is perfectly normal. It means that many of those family units are involved in that kind of work.

Usually, no comma is necessary in this sentence:

• En esa región viven setecientas familias y muchas trabajan en el campo.

Spanish often does not use a comma after an initial adverbial phrase unless the writer wants a pause, emphasis, or extra clarity.

So the version without a comma is completely normal and probably the most neutral one.

You might sometimes see:

• En esa región, viven setecientas familias...

but that is more a matter of style than necessity.

The written accent in región shows that the stress falls on the last syllable:

• re-GIÓN

Without the accent mark, Spanish stress rules would suggest a different pronunciation, so the accent is necessary.

For a native English speaker, a rough pronunciation is:

• reh-HYON or reh-GYON, depending on accent

In Spain Spanish:

• the g before i is pronounced like a throaty sound, somewhat like the ch in Scottish loch or German Bach
• so región sounds roughly like reh-khyon

The important point for learners is:

• stress the last syllable: -gión

Spanish normally uses y for and:

• familias y muchas trabajan...

It changes to e only before words that begin with an i sound:

• padres e hijos
• España e Italia

But here the next word is muchas, so there is no reason to change it:

• y muchas

So the sentence is exactly what you would expect.