For example, the Prefix Consistency and Prefix Agreement properties of $\Pi_{\mathrm{bc}}$ might not hold because:
There is a consensus divergence between node implementations (including versions of the same implementation) due to a bug, platform difference, or nondeterminism in consensus rule implementations.
This can potentially be provoked by the adversary, even if it is a corner case that would not normally happen.
In general the validity checking of snapshots made by $\Pi_{\mathrm{bft}}$ is also affected by the same divergence/nondeterminism. But the checking of whether one bc-block is a descendant of another is less likely to be incorrect/divergent than the rest of the consensus implementation, because it is much simpler and only depends on the parent fields and the block hash implementation.
If the block hash implementation has divergence/nondeterminism, all bets are off even if $\Pi_{\mathrm{bft}}$ is safe.
If the validation of proof-of-work and difficulty adjustment has divergence/nondeterminism, then there is no longer any bound on how quickly bc-blocks can be produced, and so the BFT protocol will be exposed to DoS attacks that were not otherwise possible.
The adversary has more than 50% of mining power, or less than 50% mining power but has been lucky in finding bc-blocks quickly.
Perhaps the adversary knows of a way to knock existing mining nodes offline, make them less efficient, or make their blocks less likely to be accepted, so that it has a larger proportion of the remaining mining power.
This includes partitioning some mining nodes from the rest of the network, exploiting a crash bug, or using a DoS attack to slow them down.
Partitioning attacks can be facilitated by weaknesses or exploitable inefficiencies in the peer-to-peer network protocol, or in Internet routing infrastructure and node discovery (BGP, DNS-based seeders, etc.)
Perhaps the adversary is exploiting an improved way of solving the proof-of-work.
For example, the Prefix Consistency and Prefix Agreement properties of $\Pi_{\mathrm{bc}}$ might not hold because: