Omitting the possessive case correctly

Question

I forgot how exactly the rule in English is called where you can omit the usual possessive case 's and s' if we're speaking about a row of nouns and instead just put them in front of each other (with the main noun ahead of the dependent ones).

Let's look at this example:

The redesign of units

It's a process of taking models of the old units and redesigning them to increase their quality / fix issues - gaming.

Using possessive case we can shorten it and put is as:

Units' redesign

Using the rule I mentioned in the first sentence, we can omit the s':

Units redesign

However, as far as I understand, in this case we can also omit the plural form of the word units as in this form it looks unclear whether we're talking about one unit or multiple units (which is fine):

Unit redesign

On the other hand, if we're to list the units that are about to get redesigned, can we keep that last form? I.e.

Changelog:

Unit redesign - unit 01, unit 02, unit 03

Or should it be units redesign or even unit redesigns?

Update: this isn't merely about the apostrophe rule, it's about it being omitted in certain cases too.

Answer 1

It is helpful to consider the structures of the phrases you want to compare, rather than looking at only the words that make the phrases up.

the redesign of units is a noun phrase, NP, consisting of a determiner "the" and an N-bar, N', "redesign of units". This N' is a nominalization of the V-bar, V', "redesign units". The original verb "redesign" has been converted to the noun, N, "redesign". The original direct object NP "units" has been converted to a PP "of units", because nouns cannot take direct objects.

units' redesign is a NP consisting of determiner "units'" and N' "redesign". This is another form of nominalization. The determiner consists of the NP "units" and the possessive affix "'s" (with "s's" contracted).

units redesign is a compound noun, which can also be a NP with empty determiner. Notice that with determiner "a", "a units redesign" could refer to the redesigning of units, but *"a units' redesign" is ungrammatical, because the "a" has to be inside the NP *"a units" which forms a possessive determiner after adding "'s".

unit redesign is also a compound noun, and could mean the same as "units redesign", since logical plurality is not always marked inside compounds.

To your last question, all three forms you mention are possible.

My use of the term N-bar in the above follows that of McCawley's The Syntactic Phenomena of English. Terminology might differ here for other syntactic theories.