A cache-aided erasure broadcast channel is studied. The receivers are divided into two sets: the weak and strong receivers, where the receivers in the same set all have the same erasure probability. The weak receivers, in order to compensate for the high erasure probability, are equipped with cache memories of equal size, while the receivers in the strong set have no caches. Data can be pre-delivered to weak receivers' caches over the off-peak traffic period before the receivers reveal their demands. A joint caching and channel coding scheme is proposed such that all the receivers, even the receivers without any cache memories, benefit from the presence of caches across the network. The trade-off between the cache size and the achievable rate is studied, and it is shown that the proposed scheme significantly improves the achievable trade-off upon the state-of-the-art.