her/his/their are possessive pronouns.
She has shoes (Possessing entity possesses possessed entity).
Her food is stale (Implied possessing entity possesses food which is stale).
There are two dynamics at work here.
- Use of possessive pronoun
- Use of participle action to convert a simple verb into a complex noun.
Use of present participle/gerund (~ing) to derive a possessable noun.
The use of gerunds/present participles to convert a verb into a noun is very common. This dynamic is often used to convert a original verb into a "possessable" noun.
- her beautiful painting (paint being a verb)
- her illogical thinking (verb = think)
- Her eating disorder (She has eating disorder).
- Her winning streak at 100m races. (She has a wining streak at 100m races)
The next dynamic is the implication of action.
Her act of defining the limits of bandwidth in communications earned
her world-wide recognition.
or
Her mathematics defining the limits of bandwidth in communications earned
her world-wide recognition.
Can be interestingly shortened to
Her defining the limits of bandwidth in communications earned
her world-wide recognition.
Where the possessed object is "defining the limits of bandwidth in communications".
English has a rather object-oriented tendency in the possessive, where you can place into the "variable" a constructed complex object.
{Possessive pronoun} {complex possessed entity}{rest of predicate}.
{Their}{demolishing the Bamiyan statue} {has angered the world}.
Let's look for further examples of verbs being turned into "possessable" entities.
- His {pattern of winning at horse races} has become quite well-known.
- = His {winning at horse races} has become quite well-known.
.
- His {success at winning her hand in marriage} is the culmination of many years of courtship.
- = His {winning her hand in marriage} is the culmination of many years of courtship.
.
- His {rage of foolishly killing the goose that laid golden eggs} reverted him to poverty.
- = His {foolishly killing the goose that laid golden eggs} reverted him to poverty.
.
- They were encouraged by her success at winning the prestigious award
- = They were encouraged by her winning the prestigious award
So, whenever you have doubts about the viability of a complex possessed subject, insert a relevant noun before it to validate it.
Further example
- She is considering having a baby, which is making her husband nervous.
- Her {considering having a baby} is making her husband nervous.
- Her {having a baby} has changed their life-style.
Has/have as the reflection of possession:
- Her {winning the 100m race} was exhilarating.
- She HAS {won the 100m race}, which was exhilarating.
- She POSSESSES {the event of having won the 100m race}, which was exhilarating.