How easy is it for static to damage it? I don't hear of it often so idk
The correct answer is that you should ALWAYS wear a ground strap when handling semiconductors. I usually "cheat" by touching one of the metal-cased, grounded, pieces of equipment on my workbench just before touching the electronics.
Static damage is rather rare. Most chips have some sort of static-protection, but there is limit the amount of voltage/current you can hit it with. It depends on the parts and it depends on the environment (humidity, etc.) and conditions where you are working. If every time you walk across the room and touch metal, you get a spark, you are at high-risk. But, I'm pretty sure you can damage a chip when the discharge is too small to feel or see.
It's also rather rare to run-across bad chips or unreliable chips. Once your circuit works, it should work "forever" unless you stress it with over-voltage, over-current, or over-heat. If you look-up the failure rate (MTBF), it's a LONG time... The MTBF for the Atmel chip is estimated to be almost 2000 years at normal operating temperatures! Of course, that's just an estimate since it has not existed that long, and it won't be in-use that long...
I assume that you purchased your parts from a reputable supplier, and NOT from some random seller in eBay?
I had a uln2803 fail, probably my error, I have a circuit with two 74hc595 shift registers driving two uln2803 anyway and this time a 74hc595 failed
I hate to attempt failure analysis... I always hate to guess when one of our customers asks what caused a failure...
But if the 595s that failed were both connected to the 2803 that failed, here's one possibility - You did something to overload the 2803 (something that caused too much current to flow). Then, the damaged/shorted 2803 "pulled" too much current from the 595, damaging/weakening it.
Could undervoltage harm it?
No. Over voltage (including static discharge), excess current, or excess heat. But, I have seen a power supply that would put-out a brief ~20V spike when first turned-on, before settling-down to 5V. (That's VERY RARE.)