Generally, no, the debt collector's refusal to accept a payment usually doesn't let you off the hook for the debt. Debt collectors sometimes refuse to accept payments if you can't pay the amount they want you to pay; or if they want you to give them access to your bank account, or a debit card number (which we don't recommend).
Can you please give us a little more information about your situation and why they refused payment? You can use the comments link below.