Scenario:

Customer notifies us on Sept 15 of unauthorized signature based debit card transactions.

Transactions began on August 11

Statement cut off date was August 20. Customer should have received statement no later than August 25

Claimed unauthorized transactions continue through September 10.

Is the liability still only the $50?

Generally, I'd say that since you were notified within 30 days of statement from which the first transaction occured, that the customer is not liable unless you can determine that they knew their card was missing/stolen sooner and did not notify you within 2 days.

If the transactions were "signature based" and are VISA or MC branded, the transactions are probably subject to $0 liability per their rules.