One broken spoke = warped wheel
It sounds like that spoke was carrying a lot of tension by itself. Perhaps because the wheel had been damaged previously. When the spoke failed, the nearby spokes on the side with the broken spoke weren't tight enough (or plentiful enough) to support the rim and it was pulled into the warped shape.

It could be that the way you were riding at the moment (if you were maneuvering or climbing – anything that would put an unbalanced load on the wheel) may have contributed to the sudden change of shape, or there may have been stresses in the spokes and/or rim that caused it to warp when the spoke broke. Do you know anything about the history of the wheel that might help us sort it out?

If the wheel is well built with enough spokes and a rim that is appropriate for the use and the spokes are sufficiently and evenly tensioned the failure of a single spoke shouldn't be a huge event – you might find that the rim is dragging on the brakes a bit, but I wouldn't expect anything that you couldn't patch together well enough to ride home (assuming non-extreme conditions).

The caveat is that I tend to be pretty conservative – wide rims, lots of spokes, and I'm fussy about spoke tension. So I don't know too much about spoke failures on light weight wheels with a minimal spoke count. There I would expect the failure of a single spoke to be more of a problem.