I wanted to know if you are still obligated to pay for furniture when a company is not in business anymore and can't even deal with quality issues?

If you bought the furniture on time it would have been through someone they had hired for this purpose, like a finance company. Yes, you are still obligated to pay. All the money you pay and others as well, probably goes to settle debts from this defunct (?) furniture company. You could probably call the Better Business Bureau to address your quality issues.

If you have warranty claims, write a letter and mail it to the address on your contract, return receipt requested. When it comes back to you, keep it for future use if you are sued. If you still owe money and are making monthly payments, deposit the payments into a new savings account and retain them until the balance is 'paid'. If you are sued, you will have the money ready and available.