You are well within your rights to pursue your customer. Many institutions will simply debit the thief's account for the $1,000 to collect whatever funds are remaining in the account have overdraw it by the difference. Then any additional deposits to the account will first be applied to what is owed the bank. If the funds are not repaid, pursue whatever collection efforts you normally would. If the account ever reaches a positive balance before it has to be charged off, you may want to send this customer a letter at that time saying that you will be terminating the account. (Why leave them in position to put you at additional risk.) Another suggestion is to review recent deposits to see if you have any additional liability risks from this type of activity.
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