Plant roots need air to live, surrounding roots in water drowns the plant. Left in water it will rot.

House plant containers tend not to have holes in the bottom so that you do not damage your flooring. That is a reason you need to prevent yourself over watering them.

All outdoor plant containers (should) have drainage holes as you cannot control the amount of water that they get (rain/snow).

You could always stick a few stones between the contained and plant pot to create some space between the two.

Eventually they will die because the roots need oxygen from the air spaces in the compost. If this has happened take the plant pot out of the container and put it somewhere it can drain. If the plant is already suffering it might be worth taking it out of the pot, washing most of the wet compost off and repotting it, but if it still looks OK then draining it should be sufficient. It might help to use a larger container and stand the pot on something that will raise it up a little, so that if you accidentally over water the pot has more chance of being held clear.

Everything the others have said, including it'll get rank and rot. If its a plant stood in something to catch the water, water thoroughly when it needs it, wait 30 minutes, then empty the outer pot. What the plant hasn't absorbed after 30 minutes, it doesn't need.

Agree with all the above and would point out that more plants get killed by over watering than under watering.