Has there ever been any aircraft of any type that could glide safely
with no control input simply based on the way the frame of the
aircraft was designed?
Absolutely. While many aircraft have inadequate roll stability to truly descend safely with no pilot input, especially if some turbulence is present, some aircraft do have an ample amount of roll stability as well as pitch stability. An example would be a Rogallo-style hang glider with ample sweep to the leading edges. Placing the point of connection between the pilot's body and the aircraft structure well below the aircraft CG helps to lower the effective the CG of the glider-pilot system which further increases both pitch and roll stability via the "pendulum effect", yet hang gliders have also been witnessed to fly remarkably stably when accidentally launched off a hill with no pilot attached.
Powered hang-glider-like aircraft ("trikes") can be, and have been, built on the same principles. This miniature radio-controlled model of a Rogallo-wing "trike" is extremely stable and easily capable of descending for a prolonged period, even in turbulent air, with no pilot input. Note that in this case the "trike" unit with motor and batteries is rigidly fixed in place (the position only changes when the servos move), so the "pendulum effect" is even further enhanced-- the CG of the aircraft is far below the wing.
(The "pendulum effect" is based on the fact that the drag vector, and the aerodynamic sideforce vector generated by a sideslip, both tend to exert stabilizing torques when they act above the CG of the aircraft or the aircraft-pilot system. The "pendulum effect" has also been caused the "keel effect", though this is somewhat misleading as the stabilizing action of buoyancy on a boat with a weighted keel is independent of sideslip. Some people dislike the term "pendulum effect" as well because it implies that the aerodynamic center of the aircraft is acting as some sort of a fixed pivot point, about which the weight vector or the G-load vector exerts a torque-- this is not really an accurate depiction of what is going on.)
Note that when a pilot hangs by a single flexible strap and exerts no force with his arm muscles, his body weight acts as if it is located at the point where the strap connects to the aircraft. Some early hang gliders had this connection point located well below the "keel tube" to enhance pitch and roll stability; this practice has now been discontinued because it the resulting short "hang strap" increases the muscle force that a pilot must exert to shift his weight a given distance to the side. On the other hand, in paragliders the pilot hangs by multiple suspension lines which act essentially like rigid struts due to the triangular geometry involved; in this case the pilot's body weight no longer effectively acts as if it were located at the point where the lines connect to the wing, but rather at its actual location-- which places the CG of the whole system far below the wing and creates a powerful "pendulum effect" which leads to strong roll stability, despite the anhedral geometry of the actual wing.
Paraglider pilots have often flown in clouds using only minimal instrumentation, such as a magnetic compass. Clearly this is only possible in an aircraft with strong intrinsic pitch and roll stability. On February 4 2007 paraglider pilot Ewa Wisnerska, flying without oxygen, was unintentionally lifted into a thunderstorm and survived an accidental climb in a thunderstorm to 32,000 feet above sea level followed by a descent back to earth. She was unconscious for over an hour, with her body encased in ice. When she regained consciousness her aircraft was in a stable descent.
Of course, there is an entire discipline of model-airplane-flying called "free flight". These models rise up, and then return to earth, usually landing safely, without any control input of any kind. It is instructive to examine their configuration. They almost invariably have dihedral and rather small vertical fins, and usually have a high-wing configuration.
Related ASE questions and answers:
(Q) What is the Keel Effect?
(Q) Does "pendulum effect" apply to hang gliders or any aircraft?
(A) Does "pendulum effect" apply to hang gliders or any aircraft?
(Q) Why are high-wing aircraft more stable?
(Q) How does the "pendulum effect" affect biplanes??
(Q) Does the dihedral effect happen during coordinated flight?