Sometimes a caterpillar will fall after it attaches. What to do? Some species will pupate fine laying down. Some of those, such as Monarch, must hang to finish forming or they will form with one side flat. Others, like swallowtails, do fine if they are left laying flat on a soft surface after they pupate.
When a Gulf Fritillary container built up too much moisture and several caterpillars fell after they had attached, I laid them on a coffee filter and continued feeding other caterpillars. I decided to watch and see what happened. As they pupated, I used old silk and attached them to the old silk. This works if they are freshly pupated. I left others laying on the coffee filter. The next day most had pupated and hardened without problem. Although there was a greater curve to the abdomen than normal, they emerged and flew without problem.
This method works well for swallowtails. When one has attached in the wrong place or has been found laying down before pupation, they can be laid on a coffee filter or other soft paper and they will (almost always) pupate and harden without problems.
Now, when I don’t have time to wait for them to pupate so I can reattach them, I leave them laying down.
Note: if they are left on a hard surface, such as a counter top or desk, the soft chrysalis often adheres to the surface as it hardens. When the chrysalis is moved, it either leaves part of itself attached to the surface or has a shiny deformed side. We always leave them on a soft surface, such a a paper towel, tissue, or coffee filter.