If someone is stealing your code and providing it to others to use directly from your website, aka hotlinking, then yes, they can crash your site. If the code they are using contains an image, for example, from your website, and that image is coming directly from your server, like img src="http://www.yourwebsite.com/images/yourimage.jpg, then it is your bandwidth that is allowing that code to work.
It's like using your electricity. If your neighbor somehow spliced into your electricity, and used his air conditioner and TV all the time, and one day you went to blow dry your hair, and you blew a fuse, this would be the equivalent to your site crashing. It would not come up anymore for your visitors. You, not knowing that your neighbor is stealing from you, you call the electric company to get more power. Ok, you don't do that for the electric company, but you would do that for your hosting company. And they would of course charge you for the additional use of bandwith, to prevent your site from crashing again.
How can you avoid this? Start by setting up a Google Alert for your website. Make it for www.yourwebsite.com. If code is being publicly posted somewhere for others to take and use, this will alert you to it. Next, put on some hotlink protection, which only allows specified domains to display images from your website. Learn what to consider if you do this.