Is this likely to happen on a PA28 or C172?
It’s as likely/unlikely as in any aeroplane with a propeller.
A scenario would be a Cherokee taxying and striking a prop tip crossing from grass onto concrete.
Just a little straightening required, and nobody will know.
A few hours flying later the fine crack in the blade suddenly gives way and a small piece of the propeller comes off.
It only takes a small piece to come off the tip of a propeller to unbalance it to the point where the engine is shaken off its bearers.
I once had a cam follower break up in a Cherokee 140’s O-320. It shook badly, but closing the throttle controlled the vibration.
I had a valve break in a Super Cub with an O-320, it shook too, but not as badly, likewise closing the throttle and shutting down the engine as soon as possible reduced the potential damage. (In this case rolling out on the runway).
Because I had considered what I might do, having read the report on the Owl racer over London, I was mentally prepared for what happened in the Jungmann where I did raise the nose, while switching off the mags, pushing over at around forty knots stopped the prop, kept the engine on the firewall, and reduced further damage. This was a crankshaft failure, something some Lycomings have been worried about.