If these T shirts are that "knitted" cotton fabric I wonder if it's faults in the cotton, weaknesses in the threads etc. that have broken causing the knitted fabric to come apart.
How long does it take for clothes moths to lay eggs and hatch out cloth eating grubs? Most T shirts get worn and washed very frequently which should kill and grubs. Has it has it happened with any other things you have?
I am with shysal's Posted link on this. Particular the thinner fabric.
Phoenix You do also have cats!
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