The first question is whether the business was incorporated (Inc., LLC, LLP, LP, etc.)
If the answer is no, then the business owner is liable for all the debts of the business.
If the answer is yes, then the business owner is generally only liable for:
1. Payroll taxes
(940/941) to the extent he is a signatory on the payroll account;
2. Debts which he has personally guaranteed (such as the SBA Loan) (e.g., copier leases, leases, are often guaranteed).
3. Distributions in the form of equity
(not W2 salary) taken when the company was insolvent.
He is generally not liable for debts such as utilities, phone, ad, etc. unless he has personally guaranteed them or the signature block appears to make the obligation a personal one.
Usually company "credit cards" are guaranteed by the person whose name is XXXXX XXXXX
SBA loans are typically guaranteed by the owner like you have mentioned.
I can't specifically speak to Kentucky law, but what I am describe is typical.
Let me know if I missed any portion of your question!