There is nothing special about such a property. It is simply a property of objects that are associated with a state-function from Times→States. Take any person X with associated state-function F. Then X having your example property simply means that ∀t∈Times ( X is a child at time t ∧ ∃u∈Times ( t < u ∧ X is an NBA player at time u ) ), which can be expressed using F as ∀t∈Times ( Child(F(t)) ∧ ∃u∈Times ( t < u ∧ NBAPlayer(F(u)) ) ). This is no different from properties of real-world objects in general. I think you have unconsciously made the wrong assumption that an object has different properties over time in the *logical* sense of properties. Logically, if you wish to consider each object as lasting more than a single point in time, then it cannot have different properties over its lifespan. Each object would be associated with its *entire* lifespan, and we can of course define any property of objects based on that whole lifespan.

There are in fact *many* common such real-world properties, such as "dying" and "coming" and in general any present continuous participle or perfect participle in English. There are also special adjectives that capture more complicated such properties, such as "intermittent" and "consistent". There are special adverbs that modify adjectives to yield other complicated such properties, such as "temporarily" and "repeatedly". There is no obvious limit to the complexity of such properties in natural language. For example consider "temporarily intermittent".