I don’t think that I’ve seen this particular symptom, but it is possible to damage the ICs through a few different ways. The most common way is overvoltage on the power supply pin. Make sure that your 5 V power supply really is 5 V (not an unregulated “5 V” power supply). Also make sure that you have adequate capacitors on the 5 V supply, perhaps near the ICs, so that suddenly switching off current to the LEDs does not cause a spike in the 5 V power.
Second, we have seen a symptom that _looks_ like the one that you’re describing. If you have an LED line turned “on” in the chip but are not providing current that can flow through it, it can exhibit “ghosting” for a moment after that. If you have any high-side control, it’s important to only control the LEDs to be on when there is a path for the current to flow.
