I have done that exact thing you described, although you caught the problem even before I did. I had my rear axle nuts come loose and my rear axle slip loose, and I didn't correctly diagnose it until it was so loose it threw the chain. Definitely inspect those axle nuts, keep 'em tight, and check that your wheels spin freely, regularly.
My most embarrassing story along those lines is probably when I broke my seatpost clamp, 5 miles from home. My seat post had been slipping down, so I cranked hard on the clamp to try to set it better, and I sheared the thread clean off. Needless to say, the seat immediately and for the duration of the day was all the way down and flopping side to side loosely. My Option B for that commute was more bad than riding the bike that way, so ride it I did, looking ridiculous riding super low with my knees near my chin for 5 miles in traffic. To make matters worse, I took it extra slow so as not to overburden my knees more than necessary. Not a recommended way to ride a bike, for sure.