All blockchains can suffer from consensus attacks, often referred to as 51% attacks because of the original consensus attack possible in Bitcoin. Every blockchain relies on the majority of its users or stakeholders being good actors, or at least not coordinating against the rest of the network. If the majority (or even a large minority) of the powerful network actors in a blockchain system coordinate against the rest, they will be able to launch double-spend attacks and extract large amounts of value from the network against its will.
While once theoretical, there have recently been a number of successful 51% attacks against different blockchains, such as Verge (find the link in the references). In systems that are more centralized, such as proof-of-stake systems where there may be a small number of extremely large stakeholders, it is entirely possible that similar coordination's could occur with something as simple as a few phone calls if concerned stakeholders have sufficient incentives. Such incentives do not necessarily need to be economic or on-chain at all: Politics or international relations could cause a set of patriotic stakeholders to collude for or against other users. For instance, a large amount of mining hardware and network gear originates in China, as does a lot of blockchain development. If the Chinese stakeholders discovered that they held a majority stake during an international fight with a regional rival, these stakeholders might be able to use their network power to punish network users that belong to the rival region, unilaterally.