I worked for a small company. They established a credit card in my name under the business. The company has closed down and I have charges on the credit card. Can the credit card company come after me for those charges or go after the company owner?

The credit card was obtained in your name with your permission? If so, you are responsible. You, of course, can then sue the former owners for any charges from which you did not benefit.

I agree with JudyKaytee, but it all depends on the wording in the credit agreement you signed when the card was issued to you. Typically for a corporate credit card with the employee's name on it the employee is the card holder and the employer is a co-signer. So if neither you nor your employer pay the beill they can come after both of you. But if the name on the card is the employer's, not yours, then it's your employer's debt to pay.

If it was under the business then you were just designated to use the card but it wasn't actually in your name as far as the account goes. Many companies do this with certain cards because its easier to keep track. It is the account holder who is responsible for paying the bill.

I agree you have not provided us with the info we need, who is the card issued to, the company with the company name on the card and your name as approved to sign.
Or is the card actually in your name. That makes a large difference.