2001 Corolla headlights stay on all the time even when the keys are out, any ideas?

Maybe the switch is bad like broke off inside to continually provide power

DRL module likely burned out. Just left of glove box latch hidden. Clean your battery terminals. I hacked my burned one with a single jumper wire from the only constant hot power input (greenish if I remember right, third pin over from one side) to its closest neighbor connection on the board (or the big solder ground anchor blobs) and pulled the high beam light bulb because that then stays on. Lights are now off, system finally hacked OK except for no high beam indicator. (Hi beams, lights all still work by the switch.) I haven't checked if lights are on automatically during the day yet.