When do we call a composite particle system bound? I know that to see if a system (for example, a nucleus) is a boson, we see the total spin on it. For example, an even number of protons and neutrons would make the system a composite boson. The same reasoning does not apply to electrons(For example 2 electrons are still considered fermions) as I assume the electrons are not bound together due to large distances. However, when you study about cooper pairs in superconductors, those are said to be bound and treated as bosons. My question is what is the criteria for treating a system as bound in particle physics?
 A: Not only in particle physics but quite general two objects are bound when it takes positive net energy to separate them to an infinite distance.
As an example take Newton’s laws. When an object, e.g. a space probe is bound to earth, it‘s trajectory is an ellipse and it will orbit around earth forever. It takes energy to get it to escape velocity. Then it’s trajectory becomes a hyperbola and it can escape earth’s gravitational field. “Escape” here means: it will get slower but reaching an “infinite” (i.e. huge) distance from earth it will still have velocity left.
A: Your question has nothing to do with bosons or fermions. You are asking what defines a bound system.
It is the binding energy. When there is binding energy between the parts, the system is bound. You need energy to separate them.


In quantum physics, a bound state is a special quantum state of a particle subject to a potential such that the particle has a tendency to remain localised in one or more regions of space. The potential may be external or it may be the result of the presence of another particle; in the latter case, one can equivalently define a bound state as a state representing two or more particles whose interaction energy exceeds the total energy of each separate particle.


https://en.wikipedia.org/wiki/Bound_state
