Making something means that you are connected with that object in Goblin culture, that it belongs to you and your people. If you should sell it to someone else, they get to borrow it for their lifetime.
Now, goblins have to shift along with wizarding society, so most of them don't strictly adhere to this.
Bill Weasley : "To a goblin, the rightful and true master of any object is the maker, not the purchaser. All goblin-made objects are, in goblin eyes, rightfully theirs."
Harry Potter: "But if it was bought —"
Bill Weasley : "— then they would consider it rented by the one who
had paid the money. They have, however, great difficulty with the idea
of goblin-made objects passing from wizard to wizard. You saw
Griphook's face when the tiara passed under his eyes. He disapproves.
I believe he thinks, as do the fiercest of his kind, that it ought to
have been returned to the goblins once the original purchaser died.
They consider our habit of keeping goblin-made objects, passing them
from wizard to wizard without further payment, little more than
theft."
You have very specific questions about the exact way that it works, but it simply isn't covered in that exact way.
The intricacies of who owns it (if you made it and you died, does your son now own it?) aren't precisely outlined.
However, there is a cultural touchstone that is analogous. A native American makes a blanket or artifact. This is bought by a white person and passed down in their family. When it is donated to a Sioux museum the natives say that they are glad to have it back, as though by their ancestors making it, even though they sold it, it still "belongs" to them.
From the way goblin culture is described, they have the same sort of sense of cultural ownership, albeit in a stricter, more fungible manner.
It's hard to answer the question because there's really nothing more out there. Goblin culture is covered in broad strokes, by Bill, who really only has an outsider's perspective.
We don't know how much longer if (at all) goblins live than wizards. If they lived for a thousand years each, then direct passage would be understandable, as would the desire for payment from later generations.
But, for all we know, they do have a traditional system of payment for an object that was made by a grandfather through the bloodline. Or after the maker dies, it goes to all goblins/is held by the society of goblins to be sold again or it is owned by a single person...we just don't have those answers.
It's hard for me to prove the absence of canon sources.
