BicycleBicycle

If you're riding brakeless you should always have a backup plan.
i.e. remove both of your legs from the pedals and learn how to put them on your frame and rear wheel.

This way, unless you're literally not rolling, you will be able to stop yourself.

Some riders prefer a chainstay foot position, personally, I like to huck my entire foot on top of the seat stays so I can actually skid the tire and stop.
I've had a few situations where my chain skipped off, but I don't think I've ever hit too fast of a cadence.

There was one situation where I came close...
I've hit about 36-37 mph (I had a gps speed thingy) on 45/16 gearing (I think that's near 190 rpm at the crank) and I was practically rubber legging it, but I was still (barely) able to keep up with the bike.
It felt like my legs were not really attached to my body anymore and were just spinning on their own (with my input though).
I was still able to positively apply forward motion with my leg muscles and feel them respond but it was getting to the point where I was feeling the cranks push back more than I wanted them too.
I could feel my legs getting kind of numbish and they felt "liquid" and "heavy" , more like masses of gelatin than bones and muscle.

Even 1 mph faster and I think that I would not have been able to push my legs anymore and the cranks would be pushing them instead. But instead of being nice and controllable, it felt like my legs would have just been wild spaghetti noodles flopping around.

Luckily, this was when I wasn't riding brakeless and had a front brake.
I tepidly tapped the brake out of fear of flipping over and there was almost no response, so I started to squeeze a little harder.
Normally the front brake will send you over the bars if you hold them but I eventually squeezed them as hard as I could because I wasn't slowing down.
It felt like my face was melting into my head and I had to use literally all of my strength to push against the bars to keep myself on the bike.
I finally slowed and when I touched my rim it was incredibly hot.
Needless to say I never tried that again.

I don't know what motivated me to do that in the first place. I think I was just on a really long hill and I just let go.
My intention was to keep it around 30 mph and just coast because I didn't think that my body could go that fast becuase i'm not a trained cyclist.
I thought that I would just know that I am going fast and be able to press the brakes and stop.
Anyways, that's' the best description I can give of what going too fast (for my physical limitations) on a fixed feels like.

For future reference for people that haven't done this yet, it's not a linear predictable progression as far as what/where or how fast your legs are going.
It just starts happening and it doesn't feel like you're going much faster at a certain point. If you're on a long hill, either mount a speedometer on the bars and find your physical limit on the flats, or just be very careful.

OH, I was riding shimano 105 pads and brakes at that time with the proper 105 lever too. BEST brakes i've ever ridden to this day.
I have yet to try discs though.