An O'Neill Cylinder (as defined by O'Neill, per Wikipedia) has two cylinders which are both "5 miles (8.0 km) in diameter and 20 miles (32 km) long, connected at each end by a rod via a bearing system".
Ignoring the financial cost, assume the thing got built with materials that can be created today and got launched into an extremely high orbit of Earth (say, Earth/Moon's L5 point). It spins up, gravity (1g) is felt by all (on the surface), and people living on it for 100 years or so (as self-sufficiently as possible).
Then, something bad happens, resulting in the station's permanently losing the ability to fire/power/run the engines that keep the cylinders spinning.
The bearing system connecting the cylinders is as friction-less as can be made usable in space long-term today, and the engines in their nonfunctional state don't add any friction between the cylinders.
On the one hand, it seems like the station shouldn't slow down provided that there was no net movement of mass (and that the movement was "balanced" between spinward and antispinward movement - if the trains all move antispinward, spin would increase). On the other hand, that sounds like a perpetual motion machine, since the force pushing people "down" has to come from the spin of the station (compared to Earth's gravity where "down" is caused by deformations in space, which doesn't happen on the station to an appreciable extent). One hand must be wrong, right?
How long would the inhabitants feel 1g, more than 0.9g, and more than 0.166g (the moon's gravity, again, per Wikipedia)? Or, would the station spin forever, aside from minor tidal forces and friction on the bearing (and micrometeorite impacts, etc., etc.)?