[martinkl]

The FLP result (Fischer, Lynch, Paterson) shows that consensus cannot reliably be solved in an asynchronous system (if you do not make any timing assumptions) if one or more processes can fail. The impossibility result shows that any consensus algorithm in such a system will have executions in which it waits forever and never makes a decision, which breaks the liveness property of consensus.

However, if you do allow some timing assumptions — just enough to measure a timeout, nothing more — then consensus becomes possible. In this case, the timeout is known as an "unreliable failure detector". See Chandra and Toueg's paper for details.

In a good algorithm, the safety properties do not depend on timing, only the liveness properties do. Rather than "consensus being impossible" perhaps it would be clearer to say "consensus may never terminate" in an asynchronous system. But "consensus impossible" is the standard way of phrasing this issue in the distributed systems literature.