The robust construction of the ledger data structure is an essential ingredient for the safe operation of a distributed ledger. While in traditional linear blockchain systems, permission to append to the structure is leader-based, in Directed Acyclic Graph-based ledgers, the writing access can be organised leaderless. However, this leaderless approach relies on fair treatment of non-referenced blocks, i.e. tips, by honest block issuers. We study the impact of a deviation from the standard tip selection by a subset of block issuers with the aim of halting the confirmation of honest blocks entirely. We provide models on this so-called orphanage of blocks and validate these through open-sourced simulation studies. A critical threshold for the adversary issuance rate is shown to exist, above which the tip pool becomes unstable, while for values below the orphanage decrease exponentially. We study the robustness of the protocol with an expiration time on tips, also called garbage collection, and modification of the parent references per block.