There are a few ways that competitors can steal your backlinks. One of the most common methods is to use link poaching tools. These tools allow you to search for websites that have linked to your competitors' websites. You can then contact these websites and ask them to link to your website instead.
Another common method is to use link-building tools to find broken links on other websites.
You can then reverse engineer the websites that are linking to these broken pages and let them know that the resource they are linking to no longer exists.  If you have a suitable replacement piece of content, then you can politely suggest that they change their external link to your site instead.