Ahrefs Site Audit charges 99 dollars a month for broken link scanning. This does it in the browser - HEAD every outbound link on a page, flag 4xx/5xx, show which redirects you should update at the source. Link rot accumulates ~5% of outbound links per year.
Read the story behind this tool: Why I built this - link rot is silent content degradation.
Related: Anchor-text manipulation (paired) / Redirect Chain Audit