Must be nice to be an immortal corporation that can just spin off any debts you don't want to pay, while mere mortals with finite lifespans and education debt and medical debt and credit card debt cannot unless we die.
You can never involuntarily inherit debt in the US. You have to be a co-signer to begin with.
There is nothing preventing you from doing this as an individual as well. The hard part isn’t the subsidiary or LLC, it’s getting the counter party to enter into an agreement with an entity containing no assets or long term viability.