The scenario is basically when something collides with the right kind of object and sticks to it, and functionally they should be one object from then on. I know there has to be something I can call in the collision enter method, but I just dont know what.
Parent one object to the other. Rigidbodies have a useful behavior where the colliders of child objects work in conjunction with the parent object collider to act as a single collider (this only works if the child colliders are primitive).
When you parent a rigidbody, make sure to remove the child object’s rigibody as that can lead to some weird behaviors. See Docs
create an empty gameobject, you can make a prefab of an empty object.
Then instantiate that, then addComponent(Rigidbody), then find your two gameobjects and parent them to your empty gameobject containing rigidbody.