I have 2 toilets in my house with the same problem. After flushing the toilet, the filler float gets stuck as it rises up the fill valve shaft that it sits on. The water level then rises above the float and the toilet runs continuously until I manually raise the float back up.
My question is simple. Is there a way to clean the parts or lubricate them (I doubt it) such that the float rises all the way up to stop the flow of water as it should, or do I need to replace the filler valves? I have tried adjusting the water level such that the stop mechanism triggers at lower or higher water levels, but this does not help.
The filler valves do not appear to be very old, and since it is happening to two toilets, I assume it has something to do with water quality.
The odds of having 2 toilets with the same problem is usually slim unless there is a common between them (which is your water pressure) How is your water pressure? Maybe to much or to little pressure to make them work correctly. Have you had any plumbing work done recently? You could have gotten some junk from the lines caught in the fill valves. Fill valves are cheap enough you could just replace both for $10 -$15 and see what happens.
I have had the same problem in several Kohler low flush toilets with foam tank lining. In my case I thought of lube or scale build up or cleaning but eventually discovered through trial and error that you can rotate the valve slightly to allow more clearance between the float and the tank wall and you should be good to go.