We consider the problem of privately updating a message out of $K$ messages from $N$ replicated and non-colluding databases. In this problem, a user has an outdated version of the message $\hat{W}_\theta$ of length $L$ bits that differ from the current version $W_\theta$ in at most $f$ bits. In addition, the user also has access to a cache $Z$ containing linear combinations of each of the $K$ messages, the realizations of which are unknown to the $N$ databases (unknown prefetching). The cache $Z$ contains $\ell$ linear combinations from each of the $K$ messages in the databases, and we say that $r = \frac{\ell}{L}$ is the caching ratio. The user needs to retrieve $W_\theta$ correctly using a private information retrieval (PIR) scheme with the least number of downloads without leaking any information about the message index $\theta$ to any individual database. To that end, we propose a novel achievable scheme based on \emph{syndrome decoding}. Specifically, the user downloads the syndrome corresponding to $W_\theta$, according to a linear block code with carefully designed parameters, using an optimal PIR scheme for messages with a length constraint. For this scheme, the cached linear combinations in $Z$ are chosen to be bits pertaining to the syndrome of each message in the database. We derive a lower bound on the optimal download cost for general $0 \leq r \leq 1$, and upper bounds on the optimal download cost for when $r$ is exceptionally low or high. In particular, when deriving our upper bounds, we develop novel {\it cache-aided arbitrary message length} PIR schemes. Our bounds match if the term $\log_2\left(\sum_{i=0}^f \binom{L}{i}\right)$ is an integer. Our results imply that there is a significant reduction in the download cost if $f < \frac{L}{2}$ compared with downloading $W_\theta$ directly using cached-aided PIR approaches without taking the correlation between $W_\theta$ and $\hat{W}_\theta$ into consideration.
