Speaker repair technical question

I don't have much knowledge into how speakers physically work. Recently one of my Monitor Audio gold 10 drivers went out, I found a replacement mid-woofer, while I was installing the new driver I noticed the tweeter wouldn't make any noise so I thought I had a broken crossover until I put the new driver in the speaker started working. My question is if the speaker doesn't have a woofer will the tweeter stop working and/can a broken crossover be benign and slowly blow woofers?