Consider the following facts:  

A debtor owes $50,000 to a creditor. The debtor sends a check for $30,000 and marks the check "Payment in Full."  

If the creditor deposits the check, will he/she have a right to collect the remaining balance?

There is no clear answer in law. This issue falls under the concept of "Accord and Satisfaction." This is simply an agreement to accept a payment different from what the parties contract stated.  

If the creditor accepts the tendered payment then it extinguishes the remaining balance and the claim is "satisfied" for the lesser amount.  

However, for there to be a true Accord and Satisfaction, there must first be a dispute between the parties.  

It is simply a new contract with an offer an acceptance.  

In order for there to be an Accord and Satisfaction it must be clearly stated that the amount tended is in complete satisfaction of the dispute.  

What happens if the creditor just strikes out the words "Payment in Full?"

In California there is a conflict because Civil Code Section 1526 says that the creditor can simply strike through the "Payment in Full" language and it will be ineffective.  

On the other hand, the Commercial Code Section 3311 states that the "Payment in Full" condition is binding whether or not the creditor strikes out the language.  

In the case of Directors Guild of America vs. Harmony Pictures, the court resolved the inconsistency of the two statutory sections by stating that the more recent of these enactments, mainly the commercial code would control. Accordingly, a creditor may not strike out the words "Payment in Full," cash the check, and claim the remaining balance.  

If the check is cashed in error, the creditor has 90 days to remedy the error and return the money to the debtor. In that case the debt will be reinstated. The main issue is whether the parties did in fact reach an agreement of Accordance and Satisfaction.