I was stupid and left my window open overnight with my cactus sitting next to it.:( Now it's very soft and droopy (like green swedish fish). Is there any chance of it recovering? I think it's an agave, maybe american?
Agave Americana should be able to handle temps to the low 30's. Without proper id its hard to say. I have seen some of my plants do the same thing when it get too cold. Some of them loose a limb but some are lost completely. You will know in a few days if the plant is doomed. Sorry.
If it is an Agave, it may send shoots from the mother base root, unless it was very immature (young)...