How fragile are LDR sensors - and could mine be broken?

Wired between A0 and A1, where A1 is used as ground, and using the internal pull-up of A0 to create the voltage divider.

That's probably a newbie that doesn't realise you can connect multiple things to a single ground pin... It could have been used to save battery power but then A1 should be set to INPUT or HIGH when no readings required, and that doesn't happen.

When you remove the LDR your readings should jump to 1023.