Demonstratives [Those, These] with Genitive

You can't say those's cat, even though you might be able to use those's for inanimate objects.

Although we use those as a pronominal adjective for people (i.e., those women), we don't use it as a pronoun for people; it's only used for inanimate objects and animals. Using those for people would either sound very insulting or very weird, depending on how you used it.

So you couldn't say

*See those; their cat is dead,

either. You would have to say one of

See those people; their cat is dead,
See them; their cat is dead.

And of course, those people's cat is perfectly grammatical, even though most of the time we use their cat instead.

For inanimate objects, you shouldn't use those's in formal English, but I don't think there's anything wrong with it for informal English. I can imagine somebody saying:

These jar's lids fit, but those's don't.

One addendum: you can say

I'll take care of these customers; you take care of those,

but that's because there's an implied "customers" after "those".