A thrust reverser system (110, 310) for a turbine engine, the thrust reverser system comprising: a support structure configured to be mounted to the turbine engine; a transcowl mounted on the support structure and axially translatable, relative to the support structure, between (i) a stowed position, in which the transcowl is displaced from the support structure by a first distance to form a stowed position aperture, (ii) a deployed position, in which the transcowl is displaced from the support structure a second distance that is larger than the first distance, and (iii) an over-stow position, in which the transcowl is displaced from the support structure by a third distance that is less than the first distance, thereby decreasing the size of the stowed position aperture; a door pivotally coupled to the support structure and rotatable between at least a first position, a second position, and a third position when the transcowl translates between the stowed position, the deployed position, and the over-stow position, respectively, the door configured, when it is in the second position, to redirect engine airflow to thereby generate reverse thrust; a lock coupled to the support structure and movable between a locked position, in which transcowl translation toward the deployed position is prevented, and an unlocked position, in which transcowl translation toward the deployed position is allowed, the lock configured so that it is prevented from moving from the locked position to the unlocked position when the transcowl is in the stowed position and is only able to move to the unlocked position when the transcowl is in the over-stow position; a first elastic element disposed within the stowed position aperture and engaging both the support structure and the transcowl at least when the transcowl is in and between the stowed and over-stow positions, the first elastic element configured, when engaging both the support structure and the transcowl, to supply a force to the transcowl that biases the transcowl toward the deployed position, the force in the over-stow position greater than the force in the stowed position; and a second elastic element coupled to an inner surface of the transcowl and extending into a gap that is defined between the inner surface of the transcowl and an outer surface of the door, the second elastic element sized and configured to (i) engage the door at least when the door is in the third position and (ii) supply a bias force that biases the door toward the first position at least when the door is in the third position. a support structure configured to be mounted to the turbine engine; a transcowl mounted on the support structure and axially translatable, relative to the support structure, between (i) a stowed position, in which the transcowl is displaced from the support structure by a first distance to form a stowed position aperture, (ii) a deployed position, in which the transcowl is displaced from the support structure a second distance that is larger than the first distance, and (iii) an over-stow position, in which the transcowl is displaced from the support structure by a third distance that is less than the first distance, thereby decreasing the size of the stowed position aperture; a door pivotally coupled to the support structure and rotatable between at least a first position, a second position, and a third position when the transcowl translates between the stowed position, the deployed position, and the over-stow position, respectively, the door configured, when it is in the second position, to redirect engine airflow to thereby generate reverse thrust; a lock coupled to the support structure and movable between a locked position, in which transcowl translation toward the deployed position is prevented, and an unlocked position, in which transcowl translation toward the deployed position is allowed, the lock configured so that it is prevented from moving from the locked position to the unlocked position when the transcowl is in the stowed position and is only able to move to the unlocked position when the transcowl is in the over-stow position; a first elastic element disposed within the stowed position aperture and engaging both the support structure and the transcowl at least when the transcowl is in and between the stowed and over-stow positions, the first elastic element configured, when engaging both the support structure and the transcowl, to supply a force to the transcowl that biases the transcowl toward the deployed position, the force in the over-stow position greater than the force in the stowed position; and a second elastic element coupled to an inner surface of the transcowl and extending into a gap that is defined between the inner surface of the transcowl and an outer surface of the door, the second elastic element sized and configured to (i) engage the door at least when the door is in the third position and (ii) supply a bias force that biases the door toward the first position at least when the door is in the third position.