Yes, soil erosion can influence slope failure. Erosion can weaken the stability of a slope by removing the support provided by the soil, making them more prone to failure. Erosion can also influence the stability of slopes by changing the slope angle, leading to increased potential for failure. There have been several studies that have shown that erosion can lead to slope failure.
see https://www.google.com/search?client=firefox-b-d&sxsrf=ALiCzsY3Z3MzQeYHdOtjFiKYuVXT4-V5_w:1672212986152&q=Is+there+any+cases+of+study+in+relation+to+slope+failure+caused+by+erosion+process&spell=1&sa=X&ved=2ahUKEwjy1Jzo5pv8AhUiTKQEHdjCCyEQBSgAegQICRAB&biw=1600&bih=747&dpr=1
For example, many confined or entrenched streams undercut the slope, especially on the outside of bends, and you may note vegetation leaning or tipping toward the channel due to rotational failures, or in other instances, slumps or landslides might occur with unstable soils. Gullies can deeply entrench in some landscapes, leaving the over steepened channel walls in precarious position and often increased instability.