It goes without saying that you should always do the best job you can, regardless of the assignment or the compensation; that's how you build a positive reputation (and stay employed). (An aside: Years ago an artist I had hired on multiple occasions—and paid well—casually mentioned that the quality he put into his assignments was on a sliding scale: the lower the fee, the less thought and effort he put into the art. The more he was paid, the "better" the work was he turned in. I suppose that's understandable to a degree, but...good or bad, at the end of the day it was his name on the art and his reputation on the line. The revelation also made me wonder if I was getting short-changed when I gave him assignments, that I wasn't getting his best—and eventually I came to the conclusion that I wasn't. You can guess what happened.) Anyway... if, during the course of doing a good job for your employer you create a look or style or composition or characterization that, well, seems to go beyond the brief, that goes beyond the needs (or even expectations) of the client/project, that seems to have promise, that the art could become the foundation of something that you could own and do who-knows-what with...by all means, hold onto it.
When that happens, when lightning strikes, it is no sin to put that sketch or idea in your pocket and develop it yourself on your own time. Besides, you might be the only one to see the potential in the first place: the real sin is to give something wonderful away that will go nowhere. Now, most employers might not see it quite that way, believing any ideas created on the clock belong to them, and the whole Bratz/Barbie case of a few years ago would seem to support their belief, at least to some degree. Personally, I don't buy it: an employer is paying for specific results, not abstract maybes. Any client that believes they own an artist, heart, mind, and soul...blows. Still, be a little discreet with your million-dollar-idea that you've decided to hold onto. Loose lips sink ships.
And naturally there's nothing to keep you from jotting down ideas or creating art on your own time and dime that might turn into something bigger someday. Of course, ideas are a dime a dozen and, it's as I said on another thread, it's what you do with the idea, by yourself or with collaborators, that ultimately matters. You can have a great concept and the skills to bring it to fruition, but you also have to have the drive and discipline and entrepreneurial spirit to keep plugging away until that magic moment arrives and you're able to convince audiences you've got something special to show them. Just off the top of my head, I've attached some jpegs of artist-owned properties that have been taken on lives of their own. Do you have the idea that could at some point be translated into a book series or comic or film or video game or statue or...?William Joyce's A Day With Wilbur Robinson started as a wonderful children's book and became a film, toys, game, etc.
Tony DiTerlizzi's (and Holly Black's) Spiderwick Chronicles got turned into a film with all the normal licensing spin-offs.
Mike Mignola's Hellboy has been turned into...everything! Books, films, T-shirts, toys, etc. (don't ask how much I've bought).
Joe DeVito's Kong: King of Skull Island has been translated into comics and a video game, with more projects in the works.
Jim Gurney's Dinotopia has been a book series, a TV mini-series, the source for a series of novels, and the subject of museum exhibits around the globe.