We focus on a slotted ALOHA system without feedback, in which nodes transmit time-stamped updates to a common gateway. Departing from the classical generate-at-will model, we assume that each transmitter may not always have fresh information to deliver, and tackle the fundamental question of whether sending stale packets can be beneficial from an age-of-information (AoI) standpoint. Leaning on a signal-flow-graph analysis of Markov processes the study reveals that, when packets can be lost due to channel impairments, retransmissions can indeed lower AoI for low generation rates of new information, although at a cost in terms of throughput.