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human
When nucleons bind to form a nucleus, does each nucleon "retain ownership" over its quarks (is each nucleon a truly unique entity)? Or is it possible for quarks to swap from one nucleon to another? Or does it not make sense to talk so exactly about them?

I was reading about the strong force and color confinement recently, but everything I read seemed to only talk about an isolated nucleon.  

A brief reading of the Nuclear Force (the binding force between nucleons) which can be viewed as a "residual strong force" indicates it is mediated by virtual mesons.  To my completely uneducated mind, that reads as though the nuclear force is almost like nucleons swapping quarks between one another (as a meson is a quark-antiquark pair). 

I'm assuming I'm reading too much into it and letting my uninformed imagination run a bit too wild.  Because my loose understanding of virtual particles is that they're just a byproduct of random fluctuations in the quantum fields.  But then that makes me think that maybe it doesn't make sense to say that a nucleon has "ownership" over its quarks at all, if its quarks can't really be distinguished.  Which only furthers my question of if each nucleon is clearly a separate entity while in a nucleus or not.
gpt
In short: Yes nucleons can exchange quarks via mesons, but because of confinement the baryons will always have three valence quarks.

But all, e.g., up quarks are indistinguishable. So it makes no sense to say that a particular quarks left the proton and travelled to another (as part of a pion for example). At the same time a new up-quark must have been created and remained in the original proton.

And then there is the issue of energy scale. The quarks are still bound inside the nucleons, meaning the energy required to get one out is larger than the random energy fluctuations in the system (= temperature). That is why you only exchange virtual mesons rather than real particles. Mathematically this makes it convenient to describe the nucleons as their own things that than interact with one another, rather than looking at all the quarks and gluons and whatnot separately.

You can create states of matter where the quarks are no longer bound, i.e. it makes sense to model things on the quark level. It is called "quark gluon plasma", and it exists at much higher energies/temperatures. E.g. it is created briefly in particle colliders, when you smash nuclei into each other.