A textile machine assembly includes a delivery unit and a receiving unit, wherein during operation of the textile machine assembly the delivery unit delivers a sliver to the receiving unit. A sliver storage unit is operatively configured between the delivery unit and the receiving unit to store, at least intermittently, excess sliver between the delivery unit and the receiving unit when a delivery speed of the sliver at the delivery unit is higher than a receiving speed of the sliver at the receiving unit, and to release the stored sliver when the receiving speed of the sliver at the receiving unit is higher than the delivery speed of the sliver at the delivery unit. The sliver storage unit includes a diverting unit that is movable with respect to the delivery unit or the receiving unit, wherein movement of the diverting unit changes a sliver path of the sliver from the delivery unit to the receiving unit.