A creditor is not obligated to accept any payment less than payment in full. If they accept regular payments of less than the full amount, it can be argued they have established a quasi-contract and are now bound by the payment arrangements established. That is one reason creditors will not accept partial payment or they specifically state accepting the partial payment does not establish any agreement between the parties concerning payment arrangements.
As already stated, making a payment does nothing to prohibit the creditor from suing the debtor if there is no other reason prohibiting them from suing. In fact, making a partial payment often resets the clock on the statute of limitations in many states so using your suggestion to attempt to forestall a suit actually would extend the time the creditor has to file suit.

