Uses inverse kinematics or similar animation technique that tries to dynamically find the position of joints in respect to the desired end position, usually to connect a leg to solid surface.
The first video game about Inverse kinematics was released in 1998.
Most noticeable cases are when characters are standing on slopes or stairs, where they don't unnaturally tilt with the slope or partially embed themselves in it, placing their legs somewhat naturally, angling their feet with the slope, but otherwise standing upright. Besides legs, this can also be used for moving the upper body, reaching out for buttons without forcing the player to take an exact spot (usually adjusted by the game rather than requiring the player to do so). Freely manipulating objects held in hands (with the hands visibly manipulating it), and so forth.
There's also plenty of potential for misinterpreting something that looks like inverse kinematics to be it, as with sufficient number of forward kinematic animations and some rudimentary detection code the effect can be largely indistinguishable, but that's effectively a half-way solution which should count as well.