The Definition of Done can affect the product total cost of ownership?
I'm not clear on your question, but if a Scrum Team is not adhering to the Definition of Done or is missing key aspects of it, then sure, the total cost of ownership of the product may suffer. Examples might be skipping the creation of unit tests, not holding code reviews, or not refactoring code which all result technical debt.
Rather than the Scrum Team focusing on creating value for their customers, the slow down because of technical debt. And when it comes time to paying back debt, it's more expensive to do at a later time.
And if we think of undone work, such as skipping certain aspects of quality, think about what a defect or outage may cost a company.
The later a problem is found the more expensive it is to fix. A strong Definition of Done for your product can help minimize technical debt and undone work.
The Definition of Done can affect the product total cost of ownership?
Do you have a situation in mind when it couldn't?
Sure the value(and cost as part of it) is effected by DoD and reflected in it.
What do you mean by "ownership"?
Legal ownership of the product or position of PO and his handling of Product backlog?