Can me taking my truck (2003 Chevy avalanche) mudding burn out my fuel pump? If not what are things that can burn it out?
Mudding or full throttle operation, in and of itself, should not burn out a fuel pump.
Your fuel pump is in your fuel tank. Its motor produces significant heat, and in normal use it expects to be submerged in fuel, which provides cooling by conducting heat away. If not for the fuel, the pump motor would burn out in short order.
If you keep your fuel tank level very low for mudding, and especially if you spend significant time tilted at a steep angle, this can contribute to fuel pump failure due to inadequate cooling. It’s said that 1/4 tank should be the minimum fuel level to ensure adequate fuel pump cooling.
What @MTA stated or it could just be a fuel pump in a 2003 Avalanche gave up the ghost because it was worn out. While fuel pumps last a while, given it is probably 20 years old (assuming the fuel pump was never replaced before), it was probably just its time to go. Give that thing a good and proper burial and call it a day.