From personal experience, the most common way this comes up is that you have a casual hallway conversation with a colleague, they ask "So what are you working on these days?", you tell them, and they respond with "You should talk to so-and-so, he worked on that a year ago and may have some insights" or "Have you heard about technology Foo that's designed just for that problem?" And then you follow up on that lead and realize that the project you just budgeted a week for (and will end up spending a month on, given all the unexpected problems that come up) can be solved in a couple days if you approach it slightly differently.

These are not hypotheticals - there have been numerous points in my career, ranging from being a sole technical cofounder to working in a 50K+ employee company, where a chance meeting has saved me weeks-to-months of implementation effort. And in each of those cases, the solution they suggested was not something I would've thought to look for on my own, because my starting assumption was that it needed code to solve. And similarly, it probably would not have been spotted until the feature was done and the time spent, because usually your coworkers' assumption when you embark on writing a solution is that the solution is necessary.