Broken links are bad for business or reputation. Most visitors consider stale hyperlinks to be a sign of laziness, carelessness and disrespect them. Unfortunately, if you have a large website with thousands of external links or let say a VLE with hundreds of courses and lots of external references, it's really hard to identify what external links became dead, and it's even harder to fix them because you need to know the exact location of the broken links.
I am going to give you a possible solution specially designed for our Moodle site, but you can use it on other websites as well. It is not perfect and it needs some human supervision (not 100% automated), but it is free and pretty much customisable.