An energy of $362:text{MJ}$ is stored in each of the two LHC proton beams for nominal beam parameters. This will be further increased to about $700:text{MJ}$ in the future High Luminosity LHC (HL-LHC) and uncontrolled beam losses represent a significant hazard for the integrity and safe operation of the machine. In this paper, a number of failure mechanisms that can lead to a fast increase of beam losses are analyzed. Most critical are failures in the magnet protection system, namely the quench heaters and a novel protection system called Coupling-Loss Induced Quench (CLIQ). An important outcome is that magnet protection has to be evaluated for its impact on the beam and designed accordingly. In particular, CLIQ, which is to protect the new HL-LHC triplet magnets, constitutes the fastest known failure in the LHC if triggered spuriously. A schematic change of CLIQ to mitigate the hazard is presented. A loss of the Beam-Beam Kick due to the extraction of one beam is another source of beam losses with a fast onset. A significantly stronger impact is expected in the upcoming LHC Run III and HL-LHC as compared to the current LHC, mainly due to the increased bunch intensity. Its criticality and mitigation methods are discussed. It is shown that symmetric quenches in the superconducting magnets for the final focusing triplet can have a significant impact on the beam on short timescales. The impact on the beam due to failures of the Beam-Beam Compensating Wires as well as coherent excitations by the transverse beam damper are also discussed.