There are pros who can also answer this. The bent pushrod can be from a valve sticking in the valve guide in the closed position so that the cam lobe meets an "immovable" object. Once that contest is over the pushrod is not long enough to stay engaged in the rocker dimple (.080" on my Intek 24). It can then drop out or continue to be hammered. My experience is only on my Intek, but I have read that drop out is fairly common and often you can simple replace the push rod and adjust the valve (s) Sticking is believed to be from heavy deposits in the guide (usually the exhaust valve), and is related to overheat and neglected oil. It can be aggravated by immediate shut down of overheated head.
A broken pushrod : my experience is the Intek ingested (yes, it was inside the pan) the unit, it passed through the timing gear. When I heard this I stopped immediately. A picture of the chewed/broken pushrod is in this forum. In my case I had reinstalled a head which had pushed a guide. How the pushrod launched through the oil return hole is beyond me. You have not told us how old your motor is , or if you can work on the motor.