Animations in games are typically managed by finite state machines. Each state will be set up to represent a different unique animation, keeping it simple lets say "Idle", "Walk", "Pick Up Item" and "Sit".
Certain states will be connected directly, so Idle can transition immediately into any of the other three states. Other states need to pass through states to transition, you can't go from Sit to Walk without first going to Idle because your character needs to stand firmly on two feet before they start moving.
Basically what happens when you see this "T" pose is that the code has a bug that allowed the player to go off course of the allowed states. With the Sit -> Walk transition its possible the game registers the transition out of Idle as happening, but fails to load the data for Walk. The player no longer exists in a proper state but might have transitions back into the regular sets of animations (either the transitions out of idle are still loaded, or the transitions out of walk loaded but not the animation). Until a condition is met to transition them back on track (or the game is set up with a default entry position) the game will render the character in the "T" pose or what ever pose the model maker has set the character to look like.
