We briefly review the situation around the claimed deeply bound K − states in different recent experiments and concentrate particularly on the state K − pp advocated by the FINUDA collaboration in nuclear K − absorption. We perform a theoretical simulation of the process and show that the peak in the Λ p spectrum that was interpreted as a deep K − pp bound state corresponds mostly to the process K − p p → Λ p followed by final-state interactions of the produced particles with the daughter nucleus.