Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the information capacity of each synthesis cycle and DNA storage systems in general by employing composite DNA symbols. Unlike conventional DNA storage, composite DNA encodes information in the distribution of bases across a pool of strands rather than in the individual strands themselves. Consequently, error models for DNA storage must be adapted to account for this unique characteristic. One significant error model for long-term DNA storage is strand breaks, often caused by the decay of individual bases. This work extends the strand-break channel model to the composite DNA setting. To address this challenge, we propose a coding scheme that uses marker codes to correct single strand breaks. As part of this approach, we generalise run-length-limited (RLL) codes for the composite setting and derive bounds on their redundancy.