This papers considers the coding of a source X with J decoders, each having access to a different side information Y (j). We define a new source coding problem called Extractable Source Coding with Side Information (ESC-SI). In this problem, the server stores one single coded description of the source, from which J descriptions can be extracted without re-encoding, depending on the side information available at the decoder. We want to minimize both the storage rate of the source on the server, and the J transmission rates from the server to the decoders. We provide the achievable storage-transmission rate regions for lossless source coding of general, non i.i.d., non-ergodic sources, and the achievable storage-transmission rate-distortion regions for lossy source coding for non i.i.d. Gaussian sources. The regions obtained for such general source models provide insightful design guidelines for practical applications.