"...suburbs consisting of unlawfully built houses".
I would try (as here) to shorten the sentence as much as possible. You could use home, but i sense that in this sentence it would be better to talk of housing, house or block. One lives in a home (or house too) but what you build is a house. To build a home is perhaps more poetic but it's got nothing to do with brick and timber works. Good luck :)

Use *barrios* rather than *neighborhoods*. This word is now generally recognized by English language readers as an area where poor Hispanics live, whereas *neighborhood* has a connotation of established, "anglo" homes.

I have substituted *dwellings* for *live in* + *homes*--a neat word that English that combines the whole sense very efficiently.

From Termium, for *permiso*, relating to property:

English:Property Law (Common Law)
Real Estate
Public Property
license of occupation s CORRECT
permit of occupation s CORRECT
occupation license s
licence agreement s
OBS - license of occupation; permit of occupation: terms used by parks Canada. s
1997-04-30

The sentence is not very clear to me out of context.

Puede ser que esa gente viva en casas ajenas, que no rentan. En Argentina se las llama "casa tomadas" o también puede ser que sean casa construidas ilegalmente.
¿Cómo es el contexto general?

De todos modos, ambas opciones podrían ser:

These poor people live in neighborhoods and suburbs of homes unlawfully built

or

These poor people live unlawfully in homes of neighborhoods and suburbs.

Hopes this helps! :)

If you are referring to the suburbs that grow up around cities, consisting of illegal houses (houses built without permission) then the usual term is 'shantyhouse' for 'house' and 'shantytowns' for 'suburbs'. Thus '...live in shantytowns'

However, you may wish to translate more literally. Note however, that 'home' is a very personalised concept of house, (similar to 'hogar' but not used in quite the same way) and this context seems to require 'house' rather than 'home'. For a more literal translation, in natural-sounding English I suggest:

Estos pobres viven en los barrios y suburbios de casas sin permiso = These poor/impoverished people live on the outskirts (of the city/cities) in illegally contructed houses/in houses constructed without the corresponding permits.

(Note that 'poor' in conjunction with 'people' could convey the sense of 'pobrecito', in other words, it implies a certain personal sympathy of the writer with the 'poor people' in question. If you want to be more neutral, use 'The poor' or These impoverished people').

Suerte!
Luis Luis

For clarity, I'd go with Paul.

the answers above are excellent. An additional suggestion is that you avoid "home" "permit" and "suburb" all of which have an upscale implication.

For "casa," = any of the above, or "shacks constructed, shacks put together"

"without permission (of the landowner)...." [we are not talking about city-issued permits, but rather squatters building without the permission of the owner, no?]

"barrios y suburbios" = barrios and outlying areas, fringe areas